Math 586 Spring 2008⁺ - Quantitative Finance References
and Related References

1. Yves Achdou and Olivier Pironneau, Computational Methods for Option Pricing, SIAM Books, Philadelphia, PA, 2005 (SIAM gives 30% discount for Members, including students at schools with institutional memberships or with sponsorship of a Member).
   (Publisher Description: This book is a must for becoming better acquainted with the modern tools of numerical analysis for several significant computational problems arising in finance. Important aspects of finance modeling are reviewed, involving partial differential equations and numerical algorithms for the fast and accurate pricing of financial derivatives and the calibration of parameters. The best numerical algorithms are fully explored and discussed, from their mathematical analysis up to their implementation in C++ with efficient numerical libraries. This is one of the few books that thoroughly covers the following topics: mathematical results and efficient algorithms for pricing American options; modern algorithms with adaptive mesh refinement for European and American options; regularity and error estimates are derived and give strong support to the mesh adaptivity, an essential tool for speeding up the numerical implementations; calibration of volatility with European and American options; the use of automatic differentiation of computer codes for computing greeks.)

2. Yacine Aït-Sahalia, Disentangling Diffusion from Jumps, J. Fin. Econ., vol. 74, 2004, pp.487-528.
   (Comment: Demonstrates that is very difficult, if not impossible to separated out the jumps from the diffusion when estimating market parameters.)

3. Claudio Albanese and Giuseppe Campolieti, Advanced Derivative Pricing and Risk Management: Theory, Tools, and Hands-On Programming Applications, Elsevier/Academic Press, 2006.
   This text was used by Tier for Math 586 Fall 2007 and has extensive financial analytical and computational material. (Publisher Description: Written by leading academics and practitioners in the field of financial mathematics, the purpose of this book is to provide a unique combination of some of the most important and relevant theoretical and practical tools from which any advanced undergraduate and graduate student, professional quant and researcher will benefit. This book stands out from all other existing books in quantitative finance from the sheer impressive range of ready-to-use software and accessible theoretical tools that are provided as a complete package. By proceeding from simple to complex, the authors cover core topics in derivative pricing and risk management in a style that is engaging, accessible and self-instructional. The book contains a wide spectrum of problems, worked-out solutions, detailed methodologies and applied mathematical techniques for which anyone planning to make a serious career in quantitative finance must master. In fact, core portions of the books material originated and evolved after years of classroom lectures and computer laboratory courses taught in a world-renowned professional Masters program in mathematical finance. As a bonus to the reader, the book also gives a detailed exposition on new cutting-edge theoretical techniques with many results in pricing theory that are published here for the first time.
   • Includes easy-to-implement Visual Basic for Applications (VB/VBA) numerical software libraries.
   • Proceeds from simple to complex in approaching pricing and risk management problems.
   • Provides analytical methods to derive cutting-edge pricing formulas for equity derivatives.)

4. Tor G. Andersen, L. Benzoni and J. Lund, An Empirical Investigation of Continuous-Time Equity Return Models, J. Fin., vol. 57, no. 3, 2002, pp. 1239-1284.
   (Comment: Statistical justification about why jumps and stochastic volatility are important for modeling the stock market along with the diffusion model used in the Black-Scholes model.)

5. C. A. Aourir, D. Okuyama, C. Lott and C. Eglinton, Exchanges - Circuit Breakers, Curbs, and Other Trading Restrictions , 2007.
   (Comment: NYSE circuit breakers limit large market values such as jumps by installments, casting doubt on infinite range models and gigantic crashes like in 1929 and 1987.)

6. Ludwig Arnold, Stochastic Equations: Theory and Applications, John Wiley, New York, NY, 1974.
   (Comment: Classic SDE text.)

7. Louis Bachelier, Théorie de la Spéculationi, Annales de l'Ecole Normale Supérieure, vol. 17, 1900, pp. 21-86. English translation by A. J. Boness in The Random Character of Stock Market Prices, P. H. Cootner, ed., MIT Press, Cambridge, MA, 1967, pp. 17-78.
   (Comment: Bachelier use additive Brownian motion to model option transactions of his day and was a student of Poincaré, but he work was lost in part until financial research started looking at the prior work that eventually led to the Black-Scholes model.)

8. Kerry Back, A Course in Derivative Securities: Introduction to Theory and Computation, Springer Finance, July 2005.
   (Publisher Description: This book aims at a middle ground between the introductory books on derivative securities and those that provide advanced mathematical treatments. It is written for mathematically capable students who have not necessarily had prior exposure to probability theory, stochastic calculus, or computer programming. It provides derivations of pricing and hedging formulas (using the probabilistic change of numeraire technique) for standard options, exchange options, options on forwards and futures, quanto options, exotic options, caps, floors and swaptions, as well as Visual Basic for Applications (VBA) codes implementing the formulas. It also contains an introduction to Monte Carlo, binomial models, and finite-difference methods. )

9. C. A. Ball and W. N. Torous, On Jumps in Common Stock Prices and Their Impact on Call Option Prices, J. Finance, vol. 40, 1985, pp. 155-173.
   (Comment: This paper gives empirical evidence for jump effecting call option prices.)

10. Martin Baxter and Andrew Rennie, Financial Calculus: An Introduction to Derivative Pricing, Cambridge University Press, 1996.
    (Publisher Description: Here is the first rigorous and accessible account of the mathematics behind the pricing, construction, and hedging of derivative securities. With mathematical precision and in a style tailored for market practioners, the authors describe key concepts such as martingales, change of measure, and the Heath-Jarrow-Morton model. Starting from discrete-time hedging on binary trees, the authors develop continuous-time stock models (including the Black-Scholes method). They stress practicalities including examples from stock, currency and interest rate markets, all accompanied by graphical illustrations with realistic data. The authors provide a full glossary of probabilistic and financial terms. )

11. Richard E. Bellman, Dynamic Programming, Princeton University Press, Princeton, NJ, 1957.
    (Comment: This is the original book by the founder of dynamic programming.)

12. Nicholas H. Bingham and Rudiger Kiesel, Risk-Neutral Valuation: Pricing and Hedging of Financial Derivatives, Springer Finance, May 2004.
    (Publisher Description: Since its introduction in the early 1980s, the risk-neutral valuation principle has proved to be an important tool in the pricing and hedging of financial derivatives. Following the success of the first edition of Risk-Neutral Valuation, the authors have thoroughly revised the entire book, taking into account recent developments in the field, and changes in their own thinking and teaching. In particular, the chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Levy finance, there is considerable new material on:
    • Infinite divisibility and Levy processes
    • Levy-based models in incomplete markets Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers. )

13. Tomas Björk, Arbitrage Theory in Continuous Time, Oxford Finance, May 2004.
    (Publisher Description: The second edition of this popular introduction to the classical underpinnings of the mathematics behind finance continues to combine sound mathematical principles with economic applications. Concentrating on the probabilistic theory of continuous arbitrage pricing of financial derivatives, including stochastic optimal control theory and Merton's fund separation theory, the book is designed for graduate students and combines necessary mathematical background with a solid economic focus. It includes a solved example for every new technique presented, contains numerous exercises, and suggests further reading in each chapter. In this substantially extended new edition Bjork has added separate and complete chapters on measure theory, probability theory, Girsanov transformations, LIBOR and swap market models, and martingale representations, providing two full treatments of arbitrage pricing: the classical delta-hedging and the modern martingales. More advanced areas of study are clearly marked to help students and teachers use the book as it suits their needs.)

14. Fischer Black, Fact and Fantasy in the Use of Options, Fin. Analysts. J., vol. 31, July/August 1975, pp. 36-41 and 61-72.
    (Comment: Black gives much advice on options and this paper is also the source of the so-called Black Approximation for approximating the American call option price with a stock dividend using two European can options, but the approximation is only given in words starting at the bottom of page 41.)

15. Fischer Black, How We Came Up with the Option Formula, J. Portfolio Mgmt., vol. 15, winter 1989, pp. 4-8.

16. Fischer Black and Myron Scholes, The Pricing of Options and Corporate Liabilities, J. Political Economy, vol. 81, 1973 (Spring), pp. 637-659.
    (Comment: Seminal paper, along with thorough justification the of Robert C. Merton's Spring 1973 companion paper, introduced the Black-Scholes or Black-Scholes-Merton option pricing model to the world.)

17. Richard Bookstaber, A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation, Wiley, New York, NY, 2008.
    (Comment: Bookstaber is a veteran risk manager and in particular emphasizes the role complexity plays in creating crisis, elaborating his points with examples from ecology and technology, as well as in finance.
    Publisher Description: Why do markets keep crashing and why are financial crises greater than ever before? As the risk manager to some of the leading firms on Wall Street -- from Morgan Stanley to Salomon and Citigroup -- and a member of some of the world's largest hedge funds, from Moore Capital to Ziff Brothers and FrontPoint Partners, Rick Bookstaber has seen the ghost inside the machine and vividly shows us a world that is even riskier than we think. The very things done to make markets safer, have, in fact, created a world that is far more dangerous. From the 1987 crash to Citigroup closing the Salomon Arb unit, from staggering losses at UBS to the demise of Long-Term Capital Management, Bookstaber gives readers a front row seat to the management decisions made by some of the most powerful financial figures in the world that led to catastrophe, and describes the impact of his own activities on markets and market crashes. Much of the innovation of the last 30 years has wreaked havoc on the markets and cost trillions of dollars. A Demon of Our Own Design tells the story of man's attempt to manage market risk and what it has wrought. In the process of showing what we have done, Bookstaber shines a light on what the future holds for a world where capital and power have moved from Wall Street institutions to elite and highly leveraged hedge funds.)

18. Peter Bossaerts, The Paradox of Asset Pricing, Princeton University Press, Princeton, NJ, 2002.
    (Publisher Description: Asset pricing theory abounds with elegant mathematical models. The logic is so compelling that the models are widely used in policy, from banking, investments, and corporate finance to government. To what extent, however, can these models predict what actually happens in financial markets? In The Paradox of Asset Pricing, a leading financial researcher argues forcefully that the empirical record is weak at best. Peter Bossaerts undertakes the most thorough, technically sound investigation in many years into the scientific character of the pricing of financial assets. He probes this conundrum by modeling a decidedly volatile phenomenon that, he says, the world of finance has forgotten in its enthusiasm for the efficient markets hypothesis--speculation.
    Bossaerts writes that the existing empirical evidence may be tainted by the assumptions needed to make sense of historical field data or by reanalysis of the same data. To address the first problem, he demonstrates that one central assumption--that markets are efficient processors of information, that risk is a knowable quantity, and so on--can be relaxed substantially while retaining core elements of the existing methodology. The new approach brings novel insights to old data. As for the second problem, he proposes that asset pricing theory be studied through experiments in which subjects trade purposely designed assets for real money. This book will be welcomed by finance scholars and all those math--and statistics-minded readers interested in knowing whether there is science beyond the mathematics of finance.
    This book provided the foundation for subsequent journal articles that won two prestigious awards: the 2003 Journal of Financial Markets Best Paper Award and the 2004 Goldman Sachs Asset Management Best Research Paper for the Review of Finance.)

19. Peter Bossaerts and Bernt Arne Ødegaard, Lectures on Corporate Finance, World Scientific Publishing Company; 2nd Edition, October 2006.
    (Comment: See also, Ødegaard's webpage on Financial Numerical Recipes in C⁺⁺ listed below.
    Publisher Description: A collection of lectures introducing students to the elementary concepts of corporate finance, with a systematic approach used at the Yale School of Management and the California Institute of Technology. Provides numerical examples for the concepts covered, which include dividends, capital structure, and dynamic hedging. Simple mathematics are used throughout.)

20. Phelim P. Boyle and Feidhlim Boyle, Derivatives: The Tools That Changed Finance, Risk Books, 2000.
    (Comment: There is a free chapter download at the above link. Feidhlim Boyle runs a hedge fund and is the son of Dr. Boyle.)

21. Phelim P. Boyle, Options: A Monte Carlo Approach, J. Fin. Econ., vol. 4, 1977, pp. 323-338.
    (Comment: This is a pioneering and award winning paper on the formulation of Monte Carlo simulation for financial applications.)

22. Phelim P. Boyle, M. Broadie and Paul Glasserman, Monte Carlo Methods for Security Pricing, J. Econ. Dyn. and Control, vol. 21, 1997, pp. 1267-1321.

23. René A. Carmona, Statistical Analysis of Financial Data in S-PLUS, Springer, New York, NY, 2004.
    ( Publisher Description: This book develops the use of statistical data analysis in finance, and it uses the statistical software environment of S-PLUS as a vehicle for presenting practical implementations from financial engineering. It is divided into three parts. Part I, Exploratory Data Analysis, reviews the most commonly used methods of statistical data exploration. Its originality lies in the introduction of tools for the estimation and simulation of heavy tail distributions and copulas, the computation of measures of risk, and the principal component analysis of yield curves. Part II, Regression, introduces modern regression concepts with an emphasis on robustness and non-parametric techniques. The applications include the term structure of interest rates, the construction of commodity forward curves, and nonparametric alternatives to the Black Scholes option pricing paradigm. Part III, Time Series and State Space Models, is concerned with theories of time series and of state space models. Linear ARIMA models are applied to the analysis of weather derivatives, Kalman filtering is applied to public company earnings prediction, and nonlinear GARCH models and nonlinear filtering are applied to stochastic volatility models. The book is aimed at undergraduate students in financial engineering, master students in finance and MBA's, and to practitioners with financial data analysis concerns.
    Comments: Princeton Text in Operations Research and Financial Engineering. There are online codes and data in S-Plus and now in R available online. )

24. Peter Carr and Dilip B. Madan, Option Valuation Using the Fast Fourier Transform, J. Comp. Fin., vol. 2, 1999, pp. 61-73.

25. G. Chichilnisky, Fischer Black: The Mathematics of Uncertainty, Notices of the AMS, vol. 43, no. 3, 1996, pp. 319-322.
    (Comment: Another Black obituary.)

26. Erhan Çinlar, Introduction to Stochastic Processes, Prentice-Hall, Englewood Cliffs, NJ, 1975.
    (Comment: Classic reference for Poisson jump processes.)

27. Les Clewlow and Chris Strickland, Implementing Derivative Models, Wiley Series in Financial Engineering, June 1998.
    (Publisher Description: Implementing Derivatives Models Les Clewlow and Chris Strickland Derivatives markets, particularly the over-the-counter market in complex or exotic options, are continuing to expand rapidly on a global scale, However, the availability of information regarding the theory and applications of the numerical techniques required to succeed in these markets is limited. This lack of information is extremely damaging to all kinds of financial institutions and consequently there is enormous demand for a source of sound numerical methods for pricing and hedging. Implementing Derivatives Models answers this demand, providing comprehensive coverage of practical pricing and hedging techniques for complex options. Highly accessible to practitioners seeking the latest methods and uses of models, including
    • The Binomial Method
    • Trinomial Trees and Finite Difference Methods
    • Monte Carlo Simulation
    • Implied Trees and Exotic Options
    • Option Pricing, Hedging and Numerical Techniques for Pricing Interest Rate Derivatives
    • Term Structure Consistent Short Rate Models
    • The Heath, Jarrow and Morton Model
    Implementing Derivatives Models is also a potent resource for financial academics who need to implement, compare, and empirically estimate the behaviour of various option pricing models in Finance/Investment.)

28. Rama Cont and Peter Tankov, Financial Modelling with Jump Processes, Chapman & Hall/Crc Financial Mathematics Series, December 2003.
    (Publisher Description: WINNER of a Riskbook.com Best of 2004 Book Award! During the last decade, financial models based on jump processes have acquired increasing popularity in risk management and option pricing. Much has been published on the subject, but the technical nature of most papers makes them difficult for nonspecialists to understand, and the mathematical tools required for applications can be intimidating. Potential users often get the impression that jump and Levy processes are beyond their reach. Financial Modelling with Jump Processes shows that this is not so. It provides a self-contained overview of the theoretical, numerical, and empirical aspects involved in using jump processes in financial modelling, and it does so in terms within the grasp of nonspecialists. The introduction of new mathematical tools is motivated by their use in the modelling process, and precise mathematical statements of results are accompanied by intuitive explanations. Topics covered in this book include: jump-diffusion models, Levy processes, stochastic calculus for jump processes, pricing and hedging in incomplete markets, implied volatility smiles, time-inhomogeneous jump processes and stochastic volatility models with jumps. The authors illustrate the mathematical concepts with many numerical and empirical examples and provide the details of numerical implementation of pricing and calibration algorithms. This book demonstrates that the concepts and tools necessary for understanding and implementing models with jumps can be more intuitive that those involved in the Black Scholes and diffusion models. If you have even a basic familiarity with quantitative methods in finance, Financial Modelling with Jump Processes will give you a valuable new set of tools for modelling market fluctuations.)

29. R. Dennis Cook, Regression Graphics: Ideas for Studying Regressions Through Graphics, Wiley-Interscience, New York, NY, 1998.
    (Publisher Description: An exploration of regression graphics through computer graphics. Recent developments in computer technology have stimulated new and exciting uses for graphics in statistical analyses. Regression Graphics, one of the first graduate-level textbooks on the subject, demonstrates how statisticians, both theoretical and applied, can use these exciting innovations. After developing a relatively new regression context that requires few scope-limiting conditions, Regression Graphics guides readers through the process of analyzing regressions graphically and assessing and selecting models. This innovative reference makes use of a wide range of graphical tools, including 2D and 3D scatterplots, 3D binary response plots, and scatterplot matrices. Supplemented by a companion ftp site, it features numerous data sets and applied examples that are used to elucidate the theory. Other important features of this book include:
    • Extensive coverage of a relatively new regression context based on dimension-reduction subspaces and sufficient summary plots
    • Graphical regression, an iterative visualization process for constructing sufficient regression views
    • Graphics for regressions with a binary response
    • Graphics for model assessment, including residual plots
    • Net-effects plots for assessing predictor contributions
    • Graphics for predictor and response transformations
    • Inverse regression methods
    • Access to a Web site of supplemental plots, data sets, and 3D color displays.
    An ideal text for students in graduate-level courses on statistical analysis, Regression Graphics is also an excellent reference for professional statisticians.)

30. R. Dennis Cook and Sanford Weisberg, An Introduction to Regression Graphics, Wiley-Interscience; Book & Disk edition, New York, NY, 1994.
    (Publisher Description: Covers the use of dynamic and interactive computer graphics in linear regression analysis, focusing on analytical graphics. Features new techniques like plot rotation. The authors have composed their own regression code, using Xlisp-Stat language called R-code, which is a nearly complete system for linear regression analysis and can be utilized as the main computer program in a linear regression course. The accompanying disks, for both Macintosh and Windows computers, contain the R-code and Xlisp-Stat. )

31. R. Dennis Cook and Sanford Weisberg, Applied Regression Including Computing and Graphics, Wiley Series in Probability and Statistics, New York, NY, August 6, 1999.
    (Publisher Description: A step-by-step guide to computing and graphics in regression analysis In this unique book, leading statisticians Dennis Cook and Sanford Weisberg expertly blend regression fundamentals and cutting-edge graphical techniques. They combine and up- date most of the material from their widely used earlier work, An Introduction to Regression Graphics, and Weisberg's Applied Linear Regression; incorporate the latest in statistical graphics, computing, and regression models; and wind up with a modern, fully integrated approach to one of the most important tools of data analysis. In 23 concise, easy-to-digest chapters, the authors present:? A wealth of simple 2D and 3D graphical techniques, helping visualize results through graphs:
    • An improved version of the user-friendly Arc software, which lets readers promptly implement new ideas.
    • Complete coverage of regression models, including logistic regression and generalized linear models.
    • More than 300 figures, easily reproducible on the computer.
    • Numerous examples and problems based on real data.
    • A companion Web site featuring free software and advice, available at www.wiley.com/mathematics.
    Accessible, self-contained, and fully referenced, Applied Regression Including Computing and Graphics assumes only a first course in basic statistical methods and provides a bona fide user manual for the Arc software. It is an invaluable resource for anyone interested in learning how to analyze regression problems with confidence and depth.)

32. J. M. Courtault, Y. Kabanov, B. Bru, P. Crépel, I. Lebon, and A. L. Marchand, Louis Bachelier on the Centenary of Théorie De La Spéculation, Math. Fin., vol. 10, no. 3, 2000, pp. 341-353.
    (Comment: This is about the legacy of Bachelier.)

33. John C. Cox and Mark Rubinstein, Options Markets, Prentice-Hall, February 1985.
    (Comment: One of the classic texts on option pricing.
    Publisher Description: This exploration of options markets blends institutional practice with theoretical research. Discusses theoretical models for the valuation of options and outlines trading strategies for puts and calls.)

34. Sasha Cyganowski, Lars Grüne and Peter E. Kloeden, Maple for Jump-Diffusion Stochastic Differential Equations in Finance, Programming Languages and Systems in Computational Economics and Finance, S. S. Nielsen, ed., Kluwer Academic Publishers, Amsterdam, 2002, pp. 233-269.
    (Available at http://www.uni-bayreuth.de/departments/math/~lgruene/papers/jumpfin.html.)

35. Sasha Cyganowski and Peter E. Kloeden, Maple Schemes for Jump-Diffusion Stochastic Differential Equations, Proceedings of the 16th IMACS World Congress, Lausanne 2000, M. Deville and R. Owens, eds., International Association for Mathematics and Computers in Simulation, Rutgers University, Piscataway, NJ, 2000, CD-ROM Paper 216-9, pp. 1-16.
    (Available at http://www.math.uni-frankfurt.de/~numerik/maplestoch/jumpdiff.pdf.)

36. Sasha Cyganowski, Peter E. Kloeden, and Jerzy Ombach, From Elementary Probability to Stochastic Differential Equations with Maple, Springer-Verlag, New York, NY, 2002.
    (Publisher Description: The authors provide a fast introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. The book is based on measure theory which is introduced as smoothly as possible. It is intended for advanced undergraduate students or graduates, not necessarily in mathematics, providing an overview and intuitive background for more advanced studies as well as some practical skills in the use of MAPLE in the context of probability and its applications. As prerequisites the authors assume a familiarity with basic calculus and linear algebra, as well as with elementary ordinary differential equations and, in the final chapter, simple numerical methods for such ODEs. Although statistics is not systematically treated, they introduce statistical concepts such as sampling, estimators, hypothesis testing, confidence intervals, significance levels and p-values and use them in a large number of examples, problems and simulations.)

37. Roy Davies, Gambling on Derivatives: Hedging Risk or Courting Disaster?, University of Exeter (retired), UK, January 2008.
    (Comment: Good, brief summary of financial derivative history and disasters. Some good links to other documentation too.)

38. Z. Drezner, Computation of the Bivariate Normal Integral, Mathematics of Computation, vol. 32, January 1978, 277-279.
    (Comment: Source on the Hermite Gaussian quadrature approximation used by the Hull Technical Note 5 on the Calculation of Cumulative Probability in Bivariate Normal Distribution.)

39. Darrell Duffie, Dynamic Asset Pricing Theory, Third Edition, Princeton University Press, November 1, 2001.
    (Comment: This is one of the top reference books on asset pricing.)

40. Paul Embrechts, Claudia KlŸppelberg and Thomas Mikosch, Modelling Extremal Events: for Insurance and Finance, Springer, New York, NY, 2008 (corrected edition).
    (Publisher Description: Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increasingly important role. This book sets out to bridge the gap between the existing theory and practical applications both from a probabilistic as well as from a statistical point of view. Whatever new theory is presented is always motivated by relevant real-life examples. The numerous illustrations and examples, and the extensive bibliography make this book an ideal reference text for students, teachers and users in the industry of extremal event methodology.)

41. Merran Evans, Nicholas Hastings and Brian Peacock, Statistical Distributions, 3rd ed., John Wiley, New York, NY, 2000.
    (Comment: This is a compact and very useful book about distributions and their properties.)

42. Jean-Pierre Fouque, George Papanicolaou and K. Ronnie Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, July 2000.
    (Publisher Description: This important work addresses problems in financial mathematics of pricing and hedging derivative securities in an environment of uncertain and changing market volatility. These problems are important to investors from large trading institutions to pension funds. The authors present mathematical and statistical tools that exploit the volatile nature of the market. The mathematics is introduced through examples and illustrated with simulations and the modeling approach that is described is validated and tested on market data. The material is suitable for a one-semester course for graduate students with some exposure to methods of stochastic modeling and arbitrage pricing theory in finance. The volume is easily accessible to derivatives practitioners in the financial engineering industry.)

43. Gianluca Fusai and Andrea Roncoroni, Implementing Models in Quantitative Finance: Methods and Cases, Springer Finance, February 2008.
    (Publisher Description: This book puts numerical methods into action for the purpose of solving concrete problems arising in quantitative finance. Part one develops a comprehensive toolkit including Monte Carlo simulation, numerical schemes for partial differential equations, stochastic optimization in discrete time, copula functions, transform-based methods and quadrature techniques. The content originates from class notes written for courses on numerical methods for finance and exotic derivative pricing held by the authors at Bocconi University since the year 2000. Part two proposes eighteen self-contained cases covering model simulation, derivative valuation, dynamic hedging, portfolio selection, risk management, statistical estimation and model calibration. It encompasses a wide variety of problems arising in markets for equity, interest rates, credit risk, energy and exotic derivatives. Each case introduces a problem, develops a detailed solution and illustrates empirical results. Proposed algorithms are implemented using either MATLAB or Visual Basic for Applications in collaboration with contributors.

    There are many online MATLAB and some Excel codes for most chapters available at Easylab, as well as Visual Basic for Applications (VBA) codes lised in the book.)

44. Jim Gatheral, The Volatility Surface: A Practitioner's Guide, Wiley, August 2006.
    (Publisher Description -- Praise for The Volatility Surface:
    • "I'm thrilled by the appearance of Jim Gatheral's new book The Volatility Surface. The literature on stochastic volatility is vast, but difficult to penetrate and use. Gatheral's book, by contrast, is accessible and practical. It successfully charts a middle ground between specific examples and general models--achieving remarkable clarity without giving up sophistication, depth, or breadth." --Robert V. Kohn, Professor of Mathematics and Chair, Mathematical Finance Committee, Courant Institute of Mathematical Sciences, New York University
    • "Concise yet comprehensive, equally attentive to both theory and phenomena, this book provides an unsurpassed account of the peculiarities of the implied volatility surface, its consequences for pricing and hedging, and the theories that struggle to explain it." --Emanuel Derman, author of My Life as a Quant
    • "Jim Gatheral is the wiliest practitioner in the business. This very fine book is an outgrowth of the lecture notes prepared for one of the most popular classes at NYU's esteemed Courant Institute. The topics covered are at the forefront of research in mathematical finance and the author's treatment of them is simply the best available in this form." --Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters Program in Mathematical Finance, New York University
    • "Jim Gatheral is an acknowledged master of advanced modeling for derivatives. In The Volatility Surface he reveals the secrets of dealing with the most important but most elusive of financial quantities, volatility." --Paul Wilmott, author and mathematician
    • "As a teacher in the field of mathematical finance, I welcome Jim Gatheral's book as a significant development. Written by a Wall Street practitioner with extensive market and teaching experience, The Volatility Surface gives students access to a level of knowledge on derivatives which was not previously available. I strongly recommend it." --Marco Avellaneda, Director, Division of Mathematical Finance Courant Institute, New York University
    • "Jim Gatheral could not have written a better book." --Bruno Dupire, winner of the 2006 Wilmott Cutting Edge Research Award Quantitative Research, Bloomberg LP.)

45. David Gauthier-Villars and Carrick Mollenkamp, How to Lose $7.2 Billion: A Trader's Tale (Kerviel Cooked Books, Skipped His Holidays; Calling in a Doctor), Wall Street Journal, p. A1, 02 February 2008.
    (Comment: Well told story of Jerome Kerviel, a "nut and bolts" trader, who bet the whole Société Générale bank and lost only US$7.2 billion, the most ever by a single trader.)

46. Robert Geske, The Valuation of Compound Options, J. Fin. Economics, vol. 7, 1979, pp. 63-81.
    (Comment: This paper is the background theory of compound options paper that Geske applied to his part of the RGW American option with dividend paper.)

47. Robert Geske, A Note on an Analytical Valuation Formula for Unprocted American Call Options on Stocks with Known Dividends, J. Fin. Economics, vol. 7, 1979, pp. 375-380.
    (Comment: This paper gives the "G" part of the RGW American option with dividend formula paper, correcting the "R" part of Roll and later corrected by Whaley (W).)

48. Paul Glasserman, Monte Carlo Methods in Financial Engineering, Springer, Stochastic Modelling and Applied Probability, August 2003.
    (Comment: A top refence on Monte Carlo methods in Finance.
    Publisher Description: Monte Carlo simulation has become an essential tool in the pricing of derivative securities and in risk management. These applications have, in turn, stimulated research into new Monte Carlo methods and renewed interest in some older techniques.
    This book develops the use of Monte Carlo methods in finance and it also uses simulation as a vehicle for presenting models and ideas from financial engineering. It divides roughly into three parts. The first part develops the fundamentals of Monte Carlo methods, the foundations of derivatives pricing, and the implementation of several of the most important models used in financial engineering. The next part describes techniques for improving simulation accuracy and efficiency. The final third of the book addresses special topics: estimating price sensitivities, valuing American options, and measuring market risk and credit risk in financial portfolios.
    The most important prerequisite is familiarity with the mathematical tools used to specify and analyze continuous-time models in finance, in particular the key ideas of stochastic calculus. Prior exposure to the basic principles of option pricing is useful but not essential.
    The book is aimed at graduate students in financial engineering, researchers in Monte Carlo simulation, and practitioners implementing models in industry.
    Mathematical Reviews, 2004: "... this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context.")

49. Global Derivatives,
    • Options Database
      • American Options
      • European Options
      • Compound Options
    • MATLAB Code for Simple Financial Methods
    (Comment: Great site for MATLAB financial derivative code is found at global-derivatives.com.)

50. Floyd B. Hanson, Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis, and Computation, SIAM Books: Advances in Design and Control Series, Order Code DC13 (Hanson[100]), published 03 October 2007, 28 + 441 pages, plus online appendices and sample codes.
    (Comments: There is a 30% discount with SIAM student membership and student membership is free with UIC academic membership. Chapter 12 is on Application in Financial Engineering.
    Some online material is freely available:
    • Sample Chapter (5) Stochastic Calculus for Compound Poisson Jump-Diffusions;
    • Online Appendix B Preliminaries in Probability and Analysis.
    • Post Publication Errata. Please send notice of any additional errors or queries to hanson at uic dot edu.
    Publisher Description: This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science for a clear presentation of stochastic processes and control for jump-diffusions in continuous time. The author covers the important problem of controlling these systems and, through the use of a jump calculus construction, discusses the strong role of discontinuous and nonsmooth properties versus random properties in stochastic systems. The book emphasizes modeling and problem solving and presents sample applications in financial engineering and biomedical modeling. Computational and analytic exercises and examples are included throughout. While classical applied mathematics is used in most of the chapters to set up systematic derivations and essential proofs, the final chapter bridges the gap between the applied and the abstract worlds to give readers an understanding of the more abstract literature on jump-diffusions. An additional 160 pages of online appendices are available on a Web page that supplements the book. Audience This book is written for graduate students in science and engineering who seek to construct models for scientific applications subject to uncertain environments. Mathematical modelers and researchers in applied mathematics, computational science, and engineering will also find it useful, as will practitioners of financial engineering who need fast and efficient solutions to stochastic problems.
    Contents: List of Figures; List of Tables; Preface; Chapter 1. Stochastic Jump and Diffusion Processes: Introduction; Chapter 2. Stochastic Integration for Diffusions; Chapter 3. Stochastic Integration for Jumps; Chapter 4. Stochastic Calculus for Jump-Diffusions: Elementary SDEs; Chapter 5. Stochastic Calculus for General Markov SDEs: Space-Time Poisson, State-Dependent Noise, and Multidimensions; Chapter 6. Stochastic Optimal Control: Stochastic Dynamic Programming; Chapter 7. Kolmogorov Forward and Backward Equations and Their Applications; Chapter 8. Computational Stochastic Control Methods; Chapter 9. Stochastic Simulations; Chapter 10. Applications in Financial Engineering; Chapter 11. Applications in Mathematical Biology and Medicine; Chapter 12. Applied Guide to Abstract Theory of Stochastic Processes; Bibliography; Index; A. Online Appendix: Deterministic Optimal Control; B. Online Appendix: Preliminaries in Probability and Analysis; C. Online Appendix: MATLAB Programs.)

51. Floyd B. Hanson, Stochastic Processes and Control for Jump-Diffusions, under revision, 44 pages, 22 October 2007.
    (Comments: IISc (Bangalore, INDIA) Stochastics Workshop Notes, February 2007. This is a brief tutorial on the main topics of Prof. Hanson's book, but more from the view of generalizations of ordinary differential equations to stochastic differential equations in stages, with applications. This version is very appropriate for Math 586 Spring 2008. In Top 5 Papers on Social Science Research Network in Stochastic Models.)

52. Floyd B. Hanson, Publications in Computational Finance and Bioeconomics, an annotated listing of Professor Hanson's computational finance and economics papers.

53. Desmond J. Higham, An Introduction to Financial Option Valuation, Cambridge University Press, 2004. (Comment: An excellent computational reference.
    Publisher Description: This book is intended for use in a rigorous introductory PhD level course in econometrics, or in a field course in econometric theory. It covers the measure-theoretical foundation of probability theory, the multivariate normal distribution with its application to classical linear regression analysis, various laws of large numbers, central limit theorems and related results for independent random variables as well as for stationary time series, with applications to asymptotic inference of M-estimators, and maximum likelihood theory. Some chapters have their own appendices containing the more advanced topics and/or difficult proofs. Moreover, there are three appendices with material that is supposed to be known. Appendix I contains a comprehensive review of linear algebra, including all the proofs. Appendix II reviews a variety of mathematical topics and concepts that are used throughout the main text, and Appendix III reviews complex analysis. Therefore, this book is uniquely self-contained.)

54. Desmond J. Higham and Nicolas J. Higham, MATLAB Guide, SIAM Books, 2nd Edition, 2005, Order Code OT92.
    (Comment: There is a 30% discount with SIAM student membership and student membership is free with UIC academic membership.
    Publisher Description: MATLAB is an interactive system for numerical computation that is widely used for teaching and research in industry and academia. It provides a modern programming language and problem solving environment, with powerful data structures, customizable graphics, and easy-to-use editing and debugging tools.
    This second edition of MATLAB Guide completely revises and updates the best-selling first edition and is more than 30% longer. The book remains a lively, concise introduction to the most popular and important features of MATLAB and the Symbolic Math Toolbox.
    Key features of the second edition include:
    • Aimed at both beginners and more experienced users, including students, researchers, and practitioners.
    • A tutorial in Chapter 1 gives a hands-on overview of MATLAB.
    • Thorough treatment of MATLAB mathematics, including the linear algebra and numerical analysis functions and the differential equation solvers.
    • A new chapter, Case Studies, presents more substantial examples of the use of MATLAB in a variety of modern applications.
    • A new appendix lists the 111 most useful MATLAB functions.
    • Describes MATLAB 7, but can also be used with earlier versions.
    • A Web page for the book that provides example M-files, updates, and links to MATLAB resources.)

55. John C. Hull, Options, Futures and Other Derivatives, 6th Edition, Prentice-Hall, 2005.
    See Amazon.com for less expensive used copies. (Publisher Description: Designed to bridge the gap between theory and practice, this successful book is regarded as "the bible" in trading rooms throughout the world. The books covers both derivatives markets and risk management, including credit risk and credit derivatives; forward, futures, and swaps; insurance, weather, and energy derivatives; and more. For options traders, options analysts, risk managers, swaps traders, financial engineers, and corporate treasurers.
    Widely-adopted for its comprehensive coverage, exceptionally clear explanations of difficult material, and avoidance of nonessential math, this text bridges the gap between the theory and practice of derivatives, and helps students develop a solid working knowledge of how derivatives can be analyzed. It deals with a wide range of derivative products and provides complete coverage of key analytical material. --This text refers to an out of print or unavailable edition of this title. )

56. John C. Hull, John Hull's Web Site, Rotman School of Management, University of Toronto.

57. John C. Hull, John Hull's Technical Notes for Options, Futures, and Other Derivatives, Sixth Edition, Rotman School of Management, University of Toronto.
    • Technical Note No. 4: Exact Procedure for Valuing American Calls on Dividend-Paying Stocks.
      This is the Roll, Geske, and Whaley (RGW) formula according to Hull, but likely Technical Note No. 5 will be needed to approximate the bivariate normal distribution M(a,b,rho) = Phi(a,b;rho) in the formula by Hermite Gaussian quadtature approximation.
    • Technical Note No. 5: Calculation of Cumulative Probability in Bivariate Normal Distribution .
      This is helpful for Roll, Geske, and Whaley (RGW) formula for calculating the bivariate normal distribution in Technical Note 4 using the Hermite Gaussian quadrature approxmation of fourth order in 7 significant digits of Drezner paper cited in this technical note. Note that the standard univariate normal distribution N(x) = Phi(x), so the robust MATLAB erfc function can be used:
      N(x)=Phi(x) = 0.5*erfc(-x/sqrt(2));
      or the univariate approximate version of Hull's note with his weights A(i) and nodes B(i) for i=1:4 could be used
      with f(u,x1) = exp(x1*(2*u-x1)); x1=x/sqrt(2);
      if x<=0:
      N(x)=Phi(x) = sum_{i=1:4}A(i)*f(B(i),x1);
      if x>=0:
      N(x)=Phi(x) = 1-Phi(-x) = sum_{i=1:4}A(i)*f(B(i),-x1);
      Caution: The formulas for N(x) and M(x,y,rho) in this technical notes, as in others technical notes or papers, should be verified using some known test examples like when x = 0 or x >> 1.
    • Technical Note No. 6: Differential Equation for Price of a Derivative on a Stock Providing a Known Dividend Yield .
      This is another note related to the dividend problem, but when the dividend yield is constant.

58. Peter Jaeckel, Monte Carlo Methods in Finance, Wiley, April 2002.
    (Publisher Description: An invaluable resource for quantitative analysts who need to run models that assist in option pricing and risk management. This concise, practical hands on guide to Monte Carlo simulation introduces standard and advanced methods to the increasing complexity of derivatives portfolios. Ranging from pricing more complex derivatives, such as American and Asian options, to measuring Value at Risk, or modelling complex market dynamics, simulation is the only method general enough to capture the complexity and Monte Carlo simulation is the best pricing and risk management method available.
    The book is packed with numerous examples using real world data and is supplied with a CD to aid in the use of the examples.)

59. Mark S. Joshi, C++ Design Patterns and Derivatives Pricing, Cambridge University Press, 2nd edition, June 2008.
    (Review: This is a short book, but an elegant one. It would serve as an excellent course text for a course on the practical aspects of mathematical finance.' International Statistical Institute 'This book is thought-provoking and rewarding. Even for the less experienced programmer, the presentation is readily accessible, and the coded examples can be directly used to solve real-life problems.' Journal of the American Statistics Association 'This book, although it is quite short, does cover a significant amount of material and does deal with some fairly advanced topics that are important to practitioners. The real strength of the book is its clarity and conciseness.
    SIAM Review.)

60. Mark S. Joshi, The Concepts and Practice of Mathematical Finance, Cambridge University Press, 2nd edition, November 2008.
    (Review: The book is intended as an introduction for a numerate person to the discipline of mathematical finance. In this, Mark Joshi succeeds admirably - an excellent starting point for a numerate person in the field of mathematical finance.
    Risk Magazine.)

61. Peter E. Kloeden and Eckhard Platen, Numerical Solution of Stochastic Differential Equations, Springer, Corrected Edition, November 2000.
    (Review: A most complete reference on the higher order numerical solution of diffusion SDEs.
    Publisher Description: The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations, due to the peculiarities of stochastic calculus. The book proposes to the reader whose background knowledge is limited to undergraduate level methods for engineering and physics, and easily accessible introductions to SDE and then applications as well as the numerical methods for dealing with them. To help the reader develop an intuitive understanding and hand-on numerical skills, numerous exercises including PC-exercises are included. )

62. Gary Koop, Bayesian Econometrics, Wiley, April 2003.
    (Publisher Description: Bayesian Econometrics introduces the reader to the use of Bayesian methods in the field of econometrics at the advanced undergraduate or graduate level. The book is self-contained and does not require previous training in econometrics. The focus is on models used by applied economists and the computational techniques necessary to implement Bayesian methods when doing empirical work. It includes numerous numerical examples and topics covered in the book include:
    • the regression model (and variants applicable for use with panel data)
    • time series models
    • models for qualitative or censored data
    • nonparametric methods and Bayesian model averaging
    
    Comment: Supplementary Materials, including MATLAB Scripts, Main Programs and Data Sets.)

63. Harold J. Kushner and Paul G. Dupuis, Numerical Methods for Stochastic Control Problems in Continuous Time, Springer, Stochastic Modelling and Applied Probability, December 2000.
    (Publisher Description: This book presents a comprehensive development of effective numerical methods for stochastic control problems in continuous time. The process models are diffusions, jump-diffusions, or reflected diffusions of the type that occur in the majority of current applications. All the usual problem formulations are included, as well as those of more recent interest such as ergodic control, singular control and the types of reflected diffusions used as models of queuing networks. Applications to complex deterministic problems are illustrated via application to a large class of problems from the calculus of variations. The general approach is known as the Markov Chain Approximation Method. The required background to stochastic processes is surveyed, there is an extensive development of methods of approximation, and a chapter is devoted to computational techniques. The book is written on two levels, that of practice (algorithms and applications) and that of the mathematical development. Thus the methods and use should be broadly accessible. This update to the first edition will include added material on the control of the 'jump term' and the 'diffusion term.' There will be additional material on the deterministic problems, solving the Hamilton-Jacobi equations, for which the authors' methods are still among the most useful for many classes of problems. All of these topics are of great and growing current interest.)

64. James P. LeSage, Econometrics Toolbox, Department of Economics, University of Toledo, Toledo, OH 2005. and Spatial-Econometrics.com.
    (Comment: This site contains public domain MATLAB functions for free download and use, including introduction, documentation and other information.)

65. Michael Lewis, Liar's Poker: Rising Through the Wreckage on Wall Street, Penguin, 1990.
    (Reviewer Description: As described by Lewis, liar's poker is a game played in idle moments by workers on Wall Street, the objective of which is to reward trickery and deceit. With this as a metaphor, Lewis describes his four years with the Wall Street firm Salomon Brothers, from his bizarre hiring through the training program to his years as a successful bond trader. Lewis illustrates how economic decisions made at the national level changed securities markets and made bonds the most lucrative game on the Street. His description of the firm's personalities and of the events from 1984 through the crash of October 1987 are vivid and memorable. Readers of Tom Wolfe's The Bonfire of the Vanities are likely to enjoy this personal memoir.)

66. Michael Lewis, How the Eggheads Cracked, New York Times Magazine, January 24, 1999.
    (Comment: Excellent story of the collapse of Long-Term Capital Management in 1998 and the many reasons why including copycat correlations from competing firms trading with and against LTCM. Lewis, a Wall Street veteran turned journalist, starts his story with the previous panic of 1987, which was the previous big Wall Street trading change, since you can never go back to the old trading techniques.)

67. Andrew W. Lo, Perspectives on the Current Financial Crisis, MIT Center for Transportation and Logistics, Crossroads 2009 Conference, 41 pages, March 26, 2009.
    (Comment: Perhaps the simplest explanation of the 2008 Financial Crisis, explaining the packaging of credit default derviatives in tranches (financial sausages) and much, much more. There are many copies of this talk online since Professor Lo is in high demand to give the talk. STRONGLY RECOMMENDED! )

68. Alexander Lipton, Mathematical Methods for Foreign Exchange, World Scientific, 2001.
    (Comment: Former Professor in MSCS, UIC. He is now at Merrill Lynch in London and previously was at Citadel in Chicago, but has worked at many financial institutions worldwide. This book is more general than the foreign exchange topic in the title.
    Publisher Description: Presenting a systematic and practically oriented approach to mathematical modelling in finance, particularly in the foreign exchange context, this text describes all the relevant aspects of financial engineering, including derivative pricing, in detail. The book is self-contained, with the necessary mathematical, economic and trading background carefully explained. In addition to the lucid treatment of the standard material, it describes many original results. The book can be used both as a text for students of financial engineering, and as a basic reference for risk managers, traders, and academics.)

69. Peter A. McKay, Old and New Secure: A Place at Options Table, Wall Street Journal, Tracking the Numbers: Street Sleuth Blog, January 24, 2006, Page C3.
    (Comment: Describes the transformation of The Chicago Board of Options Exchange to electronic trading of options.)

70. Alexander J. McNeil, Extreme Value Theory for Risk Managers, Internal Modelling and CAD II, RISK Books, 1999, pp. 93-113.
    (Comment: Extreme value theory is an alternate way of estimating value at risk (VaR), an estimate of probable portfolio loss. See also Embrechts et al. 2008.)

71. Robert C. Merton, Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case, Rev. Econ. Stat., vol. 51, 1969, pp. 247-257.
    (Comment: Also available in Merton's book, Chapter 4. This paper and the paper that following are pioneering papers for the optimal portfolio and consumption problem.)

72. Robert C. Merton, Optimum Consumption and Portfolio Rules in a Continuous-Time Model, J. Econ. Theory, vol. 3, no. 4 , 1971, pp. 373-413.
    (Also available in Merton's Book, Chapter 5.)

73. Robert C. Merton, Eratum, J. Econ. Theory, vol. 6, no. 2, 1973, pp. 213-214.
    (Comment: Errors in prior paper.)

74. Robert C. Merton, Theory of Rational Option Pricing, Bell J. Econ. Mgmt. Sci., vol. 4, 1973 (Spring), pp. 141-183.
    (Comment: Also available in Merton's Book, Chapter 8 and is the companion justification paper to the Black-Sholes model paper, also in the Spring of 1973, and why the model is also called the Black-Scholes-Merton model.)

75. Robert C. Merton, Option Pricing When Underlying Stock Returns are Discontinuous, J. Fin. Econ., vol. 3, 1976, pp. 125-144.
    (Also available in Merton's book, Chapter 9, and is the pioneering jump-diffusion paper in finance.)

76. Robert C. Merton, Continuous-Time Finance, Blackwell, 1990.
    (Comment: Mostly a collection of reprinted papers by one of the giants of mathematical finance.
    Publisher Description: Robert C. Merton's widely-used text provides an overview and synthesis of finance theory from the perspective of continuous-time analysis. It covers individual finance choice, corporate finance, financial intermediation, capital markets, and selected topics on the interface between private and public finance.) Robert C. Merton and Myron S. Scholes, Fischer Black, J. Finance, vol. 50, no. 5, 1996, pp. 1359-1369.
    (Comment: The Black obituary written by the two other collaborators on the Black-Scholes-Merton option pricing model and who won the Nobel Prize in Economics for in 1997, since they were the only surviving members. )

77. Thomas Mikosch, Elementary Stochastic Calculus with Finance in View, World Scientific, 1998.
    (Comment: Clearly written and short continuous-time stochastic diffusion text.)

78. Salih N. Neftci, An Introduction to the Mathematics of Financial Derivatives, Academic Press, 2000.
    (Comment: This text was used at least once by Professor Yau. John Hull and Darrell Duffie praise this book on Amazon.)

79. Numa Financial Systems, Ltd., Numa: The Internet Resource Center For Financial Derivatives.
    (Comment: Lots of useful links for References, Calculators, Indexs and more.)

80. Bernt Arne Ødegaard, Financial Numerical Recipes in C⁺⁺, Department of Financial Economics, BI Norwegian School of Management, Oslo, Norway, October 2003.
    (Comment: Nicely designed webpage of financial numerical recipies with descriptions and code from Ødegaard. Check it out, but verify as with all codes. )

81. Bernt Øksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, Universitext, June 2007.
    (Publisher Description: This book gives an introduction to the basic theory of stochastic calculus and its applications. Examples are given throughout the text, in order to motivate and illustrate the theory and show its importance for many applications in e.g. economics, biology and physics. The basic idea of the presentation is to start from some basic results (without proofs) of the easier cases and develop the theory from there, and to concentrate on the proofs of the easier case (which nevertheless are often sufficiently general for many purposes) in order to be able to reach quickly the parts of the theory which is most important for the applications. For the 6th edition the author has added further exercises and, for the first time, solutions to many of the exercises are provided. )

82. Bernt Øksendal and Agnes Sulem, Applied Stochastic Control of Jump Diffusions, Springer, December 2004.
    (Publisher Description: The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. The types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods. The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it. The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations. )

83. Options Clearing Corporation (OCC), The Equity Options Strategy Guide, The Options Industry Council (Options Education), January 2007.
    (Comment: Good options information documentations that clearly describes the profits and losses of many types of options by words and graphs. It also has explanations of may option related terms. Highly recommended for Math 586. However, the OCC will be replaced by other organizations put in place to account for the Subprime Mortgage, Investment and Banking crises.)

84. Michael Osinski, My Manhatten Project: How I Helped Build the Bomb that BlewUp Wall Street, New York Magazine, 29 March 2009.
    (Comment: How a skilled Wall Street programmer wrote the codes that made slicing up those mortgages into Collaterilized Mortgage Obligations (CMOs) and similar instruments easier for the less skilled traders and bankers to use and more critically ABUSE. An excellent short account of the 2008 (or earlier depending how you count) Wall Street and Banking Meltdown. See also the short video cartoon of his story attached to the article. )

85. Eckhard Platen and David Heath, A Benchmark Approach to Quantitative Finance, Springer Finance, 2006.
    (Comment: Publisher Description: The benchmark approach provides a general framework for financial market modeling, which extends beyond the standard risk-neutral pricing theory. It permits a unified treatment of portfolio optimization, derivative pricing, integrated risk management and insurance risk modeling. The existence of an equivalent risk-neutral pricing measure is not required. Instead, it leads to pricing formulae with respect to the real-world probability measure. This yields important modeling freedom which turns out to be necessary for the derivation of realistic, parsimonious market models. The first part of the book describes the necessary tools from probability theory, statistics, stochastic calculus and the theory of stochastic differential equations with jumps. The second part is devoted to financial modeling by the benchmark approach. Various quantitative methods for the real-world pricing and hedging of derivatives are explained. The general framework is used to provide an understanding of the nature of stochastic volatility. The book is intended for a wide audience that includes quantitative analysts, postgraduate students and practitioners in finance, economics and insurance. It aims to be a self-contained, accessible but mathematically rigorous introduction to quantitative finance for readers that have a reasonable mathematical or quantitative background. Finally, the book should stimulate interest in the benchmark approach by describing some of its power and wide applicability. )

86. Stanley R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell, 1997.
    (Comment: Professor Pliska is a co-founder of the UIC Computational Finance Track with Professors Hanson and Tier. He usually used this discrete-time finance book in one of the track main core courses, Fin 551 Financial Decision Making. Math 586 is the second main core course, but emphasizes continuous-time finance.
    Publisher Description: The purpose of this book is to provide a rigorous yet accessible introduction to the modern financial theory of security markets. The main subjects are derivatives and portfolio management. The book is intended to be used as a text by advanced undergraduates and beginning graduate students. It is also likely to be useful to practicing financial engineers, portfolio manager, and actuaries who wish to acquire a fundamental understanding of financial theory. The book makes heavy use of mathematics, but not at an advanced level. Various mathematical concepts are developed as needed, and computational examples are emphasized.)

87. William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Numerical Recipes: The Art of Scientific Computing, 3rd Edition, Cambridge University Press, September 2007.
    (Publisher Description: Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Please visit www.nr.com or www.cambridge.org/numericalrecipes for more details. New key features:
    • 2 new chapters, 25 new sections, 25% longer than Second Edition
    • Thorough upgrades throughout the text
    • Over 100 completely new routines and upgrades of many more.
    • New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector Machines
    • New Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres
    • New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions
    • An expanded treatment of ODEs with completely new routines.
    Plus comprehensive coverage of linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory
    And much, much more!)

88. William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery, Numerical Recipes (C++) Source Code CD-ROM: The Art of Scientific Computing , 3rd Edition, Cambridge University Press, September 2007.
    (Publisher Description: The Numerical Recipes Third Edition Code CDROM contains the complete source code in C++ for Numerical Recipes Third Edition, with many completely new routines, plus source code from Numerical Recipes Second Edition in C, Fortran 77, and Fortran 90 and Numerical Recipes First Edition in Pascal and BASIC, and more. Compatible with all computers and operating systems, the CDROM includes a Personal Single-User License that allows an individual to use the copyrighted code on any number of computers (no more than one at a time). More general licenses are available, as well as more information about the CDROM and the book -- including a fully electronic online version.

89. John A. Rice, Mathematical Statistics and Data Analysis, 3rd Edition, Duxbury (Thompson - Brooks/Cole), US, April 2006.
    (Publisher Description to 1st Edition: This is the first text in a generation to re-examine the purpose of the mathematical statistics course. The book's approach interweaves traditional topics with data analysis and reflects the use of the computer with close ties to the practice of statistics. The author stresses analysis of data, examines real problems with real data, and motivates the theory. The book's descriptive statistics, graphical displays, and realistic applications stand in strong contrast to traditional texts that are set in abstract settings. {Text has been used in Financial Matematics/Engineering programs at U. California Berkeley and U. Chicago. US text comes with CD of data and programs in R. There are a few financial applications.} )

90. A. J. Roberts, Elementary Calculus of Financial Mathematics, SIAM Books, Philadelphia, PA, 2005 (SIAM gives 30% discount for Members, including students at schools with institutional memberships or with sponsorship of a Member).
    (Comment: This short text is intended for an undergraduate course, but would be a good reference for beginner's in financial mathematics to get a good start in the field.
    Publisher Description: Modern financial mathematics relies on the theory of random processes in time, reflecting the erratic fluctuations in financial markets.This book introduces the fascinating area of financial mathematics and its calculus in an accessible manner geared toward undergraduate students. Using little high-level mathematics, the author presents the basic methods for evaluating financial options and building financial simulations.
    By emphasizing relevant applications and illustrating concepts with color graphics, Elementary Calculus of Financial Mathematics presents the crucial concepts needed to understand financial options among these fluctuations. Among the topics covered are the binomial lattice model for evaluating financial options, the Black Scholes and Fokker Planck equations, and the interpretation of Ito s formula in financial applications. Each chapter includes exercises for student practice and the appendices offer MATLAB® and SCILAB code as well as alternate proofs of the Fokker Planck equation and Kolmogorov backward equation. )

91. Richard Roll, An Analytical Valuation Formula for Unprotected Call Options on Stocks with Known Dividends, J. Fin. Economics, vol. 5, 1977, pp. 251-258.
    (Comment: The first paper of the RGW method, later corrected by Geske with a compound option and 2 other call options and corrected again by Whaley providing proper specification for the formulas.)

92. Rudiger U. Seydel, Tools for Computational Finance, Springer, Universitext, May 2006.
    (Publisher Description: This book is very easy to read and one can gain a quick snapshot of computational issues arising in financial mathematics. Researchers or students of the mathematical sciences with an interest in finance will find this book a very helpful and gentle guide to the world of financial engineering. SIAM review (46, 2004).
    The third edition is thoroughly revised and significantly extended. The largest addition is a new section on analytic methods with main focus on interpolation approach and quadratic approximation. New sections and subsections are among others devoted to risk-neutrality, early-exercise curves, multidimensional Black-Scholes models, the integral representation of options and the derivation of the Black-Scholes equation.
    New figures, more exercises, more background material make this guide to the world of financial engineering a real must-to-have for everyone working in FE. )

93. Steven E. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer Finance, April 2008.
    (Publisher Description: Stochastic Calculus for Finance evolved from the first ten years of the Carnegie Mellon Professional Master's program in Computational Finance. The content of this book has been used successfully with students whose mathematics background consists of calculus and calculus-based probability. The text gives both precise statements of results, plausibility arguments, and even some proofs, but more importantly intuitive explanations developed and refine through classroom experience with this material are provided. The book includes a self-contained treatment of the probability theory needed for stochastic calculus, including Brownian motion and its properties. Advanced topics include foreign exchange models, forward measures, and jump-diffusion processes. This book is being published in two volumes. This second volume develops stochastic calculus, martingales, risk-neutral pricing, exotic options and term structure models, all in continuous time. Master's level students and researchers in mathematical finance and financial engineering will find this book useful. )

94. J. Michael Steele, Stochastic Calculus and Financial Applications, Springer, June 2003.
    (Publisher Description: The Wharton School course on which the book is based is designed for energetic students who have had some experience with probability and statistics, but who have not had advanced courses in stochastic processes. Even though the course assumes only a modest background, it moves quickly and - in the end - students can expect to have the tools that are deep enough and rich enough to be relied upon throughout their professional careers. The course begins with simple random walk and the analysis of gambling games. This material is used to motivate the theory of martingales, and, after reaching a decent level of confidence with discrete processes, the course takes up the more demanding development of continuous time stochastic process, especially Brownian motion. The construction of Brownian motion is given in detail, and enough material on the subtle properties of Brownian paths is developed so that the student should sense of when intuition can be trusted and when it cannot. The course then takes up the It integral and aims to provide a development that is honest and complete without being pedantic. With the It integral in hand, the course focuses more on models. Stochastic processes of importance in Finance and Economics are developed in concert with the tools of stochastic calculus that are needed in order to solve problems of practical importance. The financial notion of replication is developed, and the Black-Scholes PDE is derived by three different methods. The course then introduces enough of the theory of the diffusion equation to be able to solve the Black-Scholes PDE and prove the uniqueness of the solution. )

95. Nassim Nicholas Taleb, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, Random House, 2nd Updated Edition, October 2008.
    (Publishers Weekly Description (of first edition): In this look at financial luck, hedge fund manager Taleb (Dynamic Hedging) addresses the apparently irrational movement of money markets around the world. Using his own investing experience and examples of others' successes and disappointments, he discusses theories like Monte Carlo math (easy; considered cheating by purists) and the concept of Russian roulette. Taleb tells interesting, well-wrought stories about individual behavior: "While Nero has succeeded beyond his wildest dreams, both personally and intellectually, he is starting to consider himself as having missed a chance somewhere." While serious investors and mathematics enthusiasts will be intrigued, readers looking for practical investment strategies will be disappointed by this rambling intellectual discourse. Tables. Copyright 2001 Cahners Business Information, Inc.)

96. Nassim Nicholas Taleb, The Black Swan, Random House, April 2007.
    (Reviewer Description: Bestselling author Nassim Nicholas Taleb continues his exploration of randomness in his fascinating new book, The Black Swan, in which he examines the influence of highly improbable and unpredictable events that have massive impact. Engaging and enlightening, The Black Swan is a book that may change the way you think about the world, a book that Chris Anderson calls, "a delightful romp through history, economics, and the frailties of human nature." See Anderson's entire guest review below.)

97. Nassim Nicholas Taleb, Ten Principles for a Black Swan-Proof World, Financial Times, April 7 2009.
    (Comment: A black swan is an a priori improbable event, until that event occurs. See his book, where he also takes more of the trader's view rather than the quantitative analyst's view.)

98. Domingo Tavella and Curt Randall, Pricing Financial Instruments: The Finite Difference Method, Wiley, April 2000.
    (Publisher Description: Numerical methods for the solution of financial instrument pricing equations are fast becoming essential for practitioners of modern quantitative finance. Among the most promising of these new computational finance techniques is the finite difference method-yet, to date, no single resource has presented a quality, comprehensive overview of this revolutionary quantitative approach to risk management.
    Pricing Financial Instruments, researched and written by Domingo Tavella and Curt Randall, two of the chief proponents of the finite difference method, presents a logical framework for applying the method of finite difference to the pricing of financial derivatives. Detailing the algorithmic and numerical procedures that are the foundation of both modern mathematical finance and the creation of financial products-while purposely keeping mathematical complexity to a minimum-this long-awaited book demonstrates how the techniques described can be used to accurately price simple and complex derivative structures.
    From a summary of stochastic pricing processes and arbitrage pricing arguments, through the analysis of numerical schemes and the implications of discretization-and ending with case studies that are simple yet detailed enough to demonstrate the capabilities of the methodology- Pricing Financial Instruments explores areas that include:
    • Pricing equations and the relationship be-tween European and American derivatives
    • Detailed analyses of different stability analysis approaches
    • Continuous and discrete sampling models for path dependent options
    • One-dimensional and multi-dimensional coordinate transformations
    • Numerical examples of barrier options, Asian options, forward swaps, and more
    With an emphasis on how numerical solutions work and how the approximations involved affect the accuracy of the solutions, Pricing Financial Instruments takes us through doors opened wide by Black, Scholes, and Merton-and the arbitrage pricing principles they introduced in the early 1970s-to provide a step-by-step outline for sensibly interpreting the output of standard numerical schemes. It covers the understanding and application of today's finite difference method, and takes the reader to the next level of pricing financial instruments and managing financial risk. )

99. Richard H. Thaler and Cass R. Sunstein, Nudge: Improving Decisions About Health, Wealth, and Happiness, Penquin paperback, February 2009.
    (Comment: More of the behavioral science view in finance and other economic areas by former U. Chicago professors.)

100. Ruey S. Tsay, Analysis of Time Series, Wiley, August 2005.
     (Comment: Text on time series by U. Chicago professor.)

101. Ramon van Handel, ACM 217: Stochastic Calculus, Filering, and Stochastic Control, Lecture Notes, CalTech Class in Appl. & Comp. Math., 265 pages, Spring 2007.
     (Comment: Author is currently a beginning faculty member at Princeton's Operation Research and Financial Engineering Department. These note are very theoretical and probably not very useful for applications, but perhaps useful for learning about abstract stochastic methods. )

102. Sanford Weisberg, Applied Linear Regression, 3rd Edition, Wiley, New York, NY, 2005.
     (Publisher Description: Applied Linear Regression, Third Edition is thoroughly updated to help students master the theory and applications of linear regression modeling. Focusing on model building, assessing fit and reliability, and drawing conclusions, the text demonstrates how to develop estimation, confidence, and testing procedures primarily through the use of least squares regression. To facilitate quick learning, this Third Edition stresses using graphical methods to find appropriate models and to better understand them. In that spirit, most analyses and homework problems use graphs for the discovery of structure as well as for the summarization of results. This text is an excellent tool for learning how to use linear regression analysis techniques to solve and gain insight into real-life problems.)

103. Tim Weithers, Foreign Exchange: A Practical Guide to the FX Markets, 3rd Edition, Wiley, New York, NY, 2006.
     (Publisher Description: In today's global marketplace, there is a critical need for both individual and professional investors to become better acquainted with foreign exchange. As economies become more intertwined and currencies continue to fluctuate, we must understand and be able to evaluate the foreign exchange (FX) markets when dealing with a variety of concerns, from consumption decisions and investment portfolios to business and retirement plans.
     Throughout his academic and professional financial careers, Tim Weithers has introduced thousands of people to the foreign exchange markets and empowered them to navigate this dynamic environment. Now, in Foreign Exchange: A Practical Guide to the FX Markets, Weithers shares his knowledge, insights, intuition, and many years of experience with you.
     Blending theory and practice, this straightforward financial primer takes the technical information commonly associated with today's FX markets and makes it more accessible. First, you'll become familiar with some of the basic elements of foreign exchangeÑmajor currencies, bid-ask spreads, and the importance of interest ratesÑas well as gain some historical perspective on the evolution and development of the FX markets. After this introductory overview, you'll receive a detailed description of the products, techniques, and strategies that can be used to master the foreign exchange markets.
     Topics discussed within the following pages include:
     • The foreign exchange spot market
     • FX forwards and futures
     • Cross-currency interest rate swaps
     • FX options, structured products, and exotic options
     • The economics of exchange rates and international trade
     • Currency crises
     • Modern developments
     • And much more
     With this book as your guide, you'll also gain a solid understanding of how the FX market and its instruments work; acquire an ability to look beyond the noise of news reports and stories presented by the popular media and financial press; and learn how to avoid some of the most common mistakes made in today's FX markets.
     Filled with in-depth insights and helpful recommendations, and backed by numerous examples and exercises, Foreign Exchange frames the FX market in practical economic terms that can help you make sense of this ever-evolving, and often confusing, environment.)

104. Robert E. Whaley, On the Valuation of American Call Options on Stocks with Known Dividends, J. Fin. Economics, vol. 9, 1981, pp. 207-211.
     (Comment: The last paper of the RGW method, finally corrected by Whaley providing proper specification for the formuls. See also Hull's Tech. Note 4 on the RGW method.)

105. Paul Wilmott, Sam Howison and Jeff Devine, Mathematics of Financial Derivatives, A Student Introduction, Cambridge University Press, 1995.
     (Comment: One of the oldest Math 586 texts. Wilmott has a long series of much larger texts that he updates every several year under different titles.

     Publisher Description: Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "real-world" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation. The authors present a unified approach to modeling derivative products as partial differential equations, using numerical solutions where appropriate. The authors assume some mathematical background, but provide clear explanations for material beyond elementary calculus, probability, and algebra. This volume will become the standard introduction for advanced undergraduate students to this exciting new field.)

106. Paul Wilmott, Paul Wilmott on Quantitative Finance, 3 Volume Set, 2nd Edition, Wiley, March 2006.
     (Publisher Description: Volume 1: Mathematical and Financial Foundations; Basic Theory of Derivatives; Risk and Return. The reader is introduced to the fundamental mathematical tools and financial concepts needed to understand quantitative finance, portfolio management and derivatives. Parallels are drawn between the respectable world of investing and the not-so-respectable world of gambling.
     Volume 2: Exotic Contracts and Path Dependency; Fixed Income Modeling and Derivatives; Credit Risk In this volume the reader sees further applications of stochastic mathematics to new financial problems and different markets.
     Volume 3: Advanced Topics; Numerical Methods and Programs. In this volume the reader enters territory rarely seen in textbooks, the cutting-edge research. Numerical methods are also introduced so that the models can now all be accurately and quickly solved.
     Throughout the volumes, the author has included numerous Bloomberg screen dumps to illustrate in real terms the points he raises, together with essential Visual Basic code, spreadsheet explanations of the models, the reproduction of term sheets and option classification tables. In addition to the practical orientation of the book the author himself also appears throughout the bookin cartoon form, readers will be relieved to hearto personally highlight and explain the key sections and issues discussed. )