Math 586 Spring 2008 - Quantitative Finance References
and Related References

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

2. 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 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.)

3. 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.
   (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.)

4. C. A. Aourir, D. Okuyama, C. Lott and C. Eglinton, Exchanges - Circuit Breakers, Curbs, and Other Trading Restrictions , 2007.
   (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.)

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

6. 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.
   (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.).

7. 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 VBA code implementing the formulas. It also contains an introduction to Monte Carlo, binomial models, and finite-difference methods. )

8. 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.
   (This paper give empirical evidence for jump effecting call option prices.)

9. 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. )

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

11. 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. )

12. Tomas Bjork, 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.)

13. Fischer Black, Fact and Fantasy in the Use of Options, Fin. Analysts. J., vol. 31, July/August 1975, pp. 36-41 and 61-72.
    (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.)

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

15. Fischer Black and Myron Scholes, The Pricing of Options and Corporate Liabilities, J. Political Economy, vol. 81, 1973 (Spring), pp. 637-659.

16. P. 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.)

17. Peter Bossaerts and Bernt Arne Ødegaard, Lectures on Corporate Finance, World Scientific Publishing Company; 2nd Edition, October 2006.
    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.)

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

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

20. 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.

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

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

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

24. 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. Finance/Investment )

25. 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. )

26. 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. (This is about the legacy of Bachelier.)

27. John C. Cox and Mark Rubinstein, Options Markets, Prentice-Hall, February 1985.
    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.)

28. 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.)

29. 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.)

30. 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.)

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

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

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

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

35. Jean-Pierre Fouque, George Papanicolaou and K. Ronnie Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cmbridge 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.)

36. 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.)

37. 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.
    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.

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

39. 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.
    (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).)

40. Paul Glasserman, Monte Carlo Methods in Financial Engineering, Springer, Stochastic Modelling and Applied Probability, August 2003.
    (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.")

41. Global Derivatives,
    • Options Database
      • American Options
      • European Options
      • Compound Options
    • MATLAB Code for Simple Financial Methods

42. 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.
    (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.)

43. Floyd B. Hanson, Stochastic Processes and Control for Jump-Diffusions, under revision, 44 pages, 22 October 2007.
    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.)

44. Floyd B. Hanson, Publications in Computational Finance and Bioeconomics.

45. Desmond J. Higham, An Introduction to Financial Option Valuation, Cambridge University Press, 2004. 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. )

46. Desmond J. Higham and Nicolas J. Higham, MATLAB Guide, SIAM Books, 2nd Edition, 2005, Order Code OT92.
    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.)

47. 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. )

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

49. 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.

50. 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. )

51. 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.)

52. Alexander Lipton, Mathematical Methods for Foreign Exchange, World Scientific, 2001. (Former Professor in MSCS, UIC. He is not 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.)

53. 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.
    Describes the transformation of The Chicago Board of Options Exchange to electronic trading of options.

54. Robert C. Merton, Lifetime Portfolio Selection Under Uncertainty: The Continuous-Time Case, Rev. Econ. Stat., vol. 51, 1969, pp. 247-257.
    (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.)

55. 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.)

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

57. Robert C. Merton, Theory of Rational Option Pricing, Bell J. Econ. Mgmt. Sci., vol. 4, 1973 (Spring), pp. 141-183.
    (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.)

58. 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.)

59. Robert C. Merton, Continuous-Time Finance, Blackwell, 1990.
    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.
    (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.)

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

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

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

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

64. 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. )

65. 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. )

66. Options Clearing Corporation (OCC), The Equity Options Strategy Guide, The Options Industry Council (Options Education), January 2007. 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.

67. Stanley R. Pliska, Introduction to Mathematical Finance: Discrete Time Models, Blackwell, 1997.
    Professor Pliska is a co-founder of the 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.)

68. 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!)

69. 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.

70. Richard Roll, An Analytical Valuation Formula for Unprotected Call Options on Stocks with Known Dividends, J. Fin. Economics, vol. 5, 1977, pp. 251-258.
    (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 formuls.)

71. 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. )

72. 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. )

73. 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. )

74. Robert E. Whaley, On the Valuation of American Call Options on Stocks with Known Dividends, J. Fin. Economics, vol. 9, 1981, pp. 207-211.
    (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.)

75. Paul Wilmott, Sam Howison and Jeff Devine, Mathematics of Financial Derivatives, A Student Introduction, Cambridge University Press, 1995.
    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.

76. 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. )