• Instructor: Floyd B. Hanson (hanson at math at uchicago dot edu).
  • Office Hour: Monday, time (5PM?), FinMath Lounge/Lab E7; weeks 3 & 4 in Singapore.
  • Webpages:
    • F. B. Hanson Short Homepage, Financial Mathematics Program, University of Chicago.

    • F. B. Hanson Long Home Page, Professor Emeritus, Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago.

• Chicago Teaching Assistants:
  1. Sunil Kumar (sunil at uchicago dot edu).
  2. Dan Wang (danwang at uchicago dot edu).
  3. Jin Zhang (jzhang26 at uchicago dot edu).
  4. Ting Zhang (tingzhang at uchicago dot edu).
     • Office Hours: 5:30 to 6:30 on Friday at E117
     • Review Sessions: TBA

• Singapore Teaching Assistants:
  1. Wei Khing For (weikhing at uchicago dot edu).
  2. Sanjeet Singh (sanjeet at uchicago dot edu).
  3. Ronnie Thomas (ronniethomas at uchicago dot edu).
     • Office Hours: Thursdays from 6:00pm - 7:00pm
     • Review Sessions: TBA

• UBS Stamford CT Teaching Assistant:
  1. Manuel Zamfir (t-9manue at uchicago dot edu).
     • Office Hour: TBA
     • Review Session: TBA

• Class Webpage (tentative):
  http://www.math.uchicago.edu/~hanson/finm345
  OR
  http://finmath.uchicago.edu/new/msfm/current/finm345a09.html
  on Financial Mathematics Program, Current Students.

• Texts:
  • Primary Text: FINM 345 Lecture Notes, Autumn 2009,
    usually each lecture is posted on Chalk before each lecture;
    FINM 331 Lecture Notes:
    • L1;    L2;    L3;    L4;    L5;    L6;    L7;    L8;    L9;    L10;   

  • Optionally recommended:
    • Floyd B. Hanson, Applied Stochastic Processes and Control for Jump-Diffusions: Modeling, Analysis, and Computation, SIAM Books, October 2007. (Comments: There is a 30% discount with SIAM student membership, but you can get a Text and Order Page with Coupon Code BKUC09, special for this class. Amazon and other book sellers charge list price.
      Alert: Have arranged a special SIAM nonmember-institution student 30%? discount, but coupon code will be posted later!)

      Some online material is freely available:

      • Sample Chapter (5) Stochastic Calculus for Compound Poisson Jump-Diffusions;
      • Online Appendix B Preliminaries in Probability and Analysis.
      • Online Appendix C: MATLAB Code Listings: Generating Figures, 46 pages.
        • MATLAB Source Codes Table of Contents.
        • MATLAB Source Codes Directory, 27 files plus directory zipped.
      • Post Publication Errata. (Please send notice of any additional errors or queries to hanson at uic dot edu).
    • Ruey S. Tsay, Analysis of Time Series, Wiley, August 2005. (Comments: Text on time series by U. Chicago business professor; we will have a short introduction of time series in the context of stochastic calculus, but moved from FinM 331 Winter 2009 and will not be in Winter 2010.)

  • Optional:
    • Steven E. Shreve Stochastic Calculus for Finance II: Continuous-Time Models, Springer Finance, April 2008. (This is the Carnegie Mellon Computational Finance course, but is more abstract and much less applied, primarily about diffusions, getting to jumps much later in the book; however, this book is often used in the Financial Mathematics courses here.)

  • Recommended Computational System: MATLAB;
    • Desmond J. Higham and Nicolas J. Higham, MATLAB Guide, SIAM Books, 2nd Edition, 2005, Order Code OT92. (Comments: There is a 30% discount with SIAM student membership, but you can get a complimentary membership if sponsored by a SIAM member. This is probably the best mathematical MATLAB book.)
    • Also, R, S and Excel are acceptable for assignments, but you are on your own.

• Grading:
  • Homework:
    1. There will be about 8-10 graded homework sets, and perhaps several projects:
       • HW1;    HW2;    HW3;    HW4;    HW5;    HW6;    HW7;    HW8;    HW9;   
    2. A student may consult with other student about the ideas involved, but submitted homework must be the individual student's own work and expression.
    3. Nearly identical solutions, i.e., copies, will receive discounted grades with divided credit as if one problem.
    4. Codes and/or worksheets need to be submitted with computational solutions.
    5. Graphs should be professionally done with titles, axes labels and short description or caption.
    6. Homework submitted via Chalk should have a unique name, e.g., <CNETusername>_HW<N>.pdf, where is the homework number.
  • Exams: There will be a final exam, take-home:
    THFExam10;   
  • Final Grade: The grade will be based upon an average of homework and final exam scores, weighted to reflect the number of points involved, i.e., homework will substantially count.

(Comments: This will be a more applied course than in the past, starting from stochastic differentials and stochastic integrals, as in the regular calculus, except with basic probabilities, then building up to stochastic differential equations and their solutions, eventually leading to financial applications and some useful abstract notions in stochastic calculus.

Knowledge of basic probability is assumed, but you can review background preliminaries from online sources given below.)

1. Introduction to Stochastic Diffusion and Jump Processes: Basic properties of Poisson and Wiener stochastic processes. Based on the calculus model, differential and incremental models are discussed. The continuous Wiener processes model the background or central part of of financial distributions, while the Poisson jump process models the extreme, long tail behavior of crashes and bubbles of financial distributions. ... 1-2 Lectures

2. Stochastic Integration for Stochastic Differential Equations: While the stochastic differentials and increments are useful in developing stochastic models and numerically simulating solutions, stochastic integration is important for getting explicit solutions or more manageable forms. ... 1 Lecture

3. Elementary Stochastic Differential Equations (SDEs): The stochastic chain rules for jump-diffusions with simple Poisson jump processes, starting from diffusion chain rules to jump chain rules to jump-diffusion chain rules. Time-varying coefficients are also considered. ... 2 Lectures

4. Stochastic Differential Equations for General Jump-Diffusions: Stochastic differential equations with compound Poisson processes, i.e., including randomly distributed jump-amplitudes, state-time dependent coefficients, multi-dimensional SDEs, Martingales and finite rate Levy jump-diffusion formulations. ... 2-3 Lectures

5. Applications to Financial Engineering: Generalized Black-Scholes-Merton option pricing analysis, option pricing for jump-diffusions and stochastic volatility, using risk-neutral measures; also the important event Greenspan process. Of course, financial models and motivations will be used throughout the course. ... 1-2 Lectures

6. Time Series Introduction and the relationship to SDE models: Time series models such as the discrete AR (autoregressive), MA (moving average), ARMA (combined), and ARCH (conditional "volatility") models, as time allows. ... 1-2 Lectures

• Introductory Probability: see for instance,
  • F. B. Hanson, Online Appendix B Preliminaries in Probability and Analysis ,

  • Niels O. Nygaard, Introduction to Stochastic Processes, a concise review of background measure theory, probability theory and stochastic processes, but more abstract than in this course.

• Very Basic MATLAB:
  • The MATLAB Student Version comes with the statistics and other toolboxes. However, MATLAB will be introduced in the course as examples and demonstration codes will be given in the lectures as well as posted online. Heavily rely on MATLAB Help Windows.

  • See also Hanson's Online MATLAB Programs mentioned above.

  • See also Professor Nygaard's review sessions on various topics, in particular on statistics.

• Hanson's Related Prior Courses:
  • Math 586 Computational Finance, UIC, Spring Semester 2008.
  • Applied Optimal Control, with emphasis on the control of jump-diffusion stochastic processes, UIC, Fall 2006. (First part of course was on stochastic processes and his book was written for this course and several related courses.)

• Hanson's Quantitative Finance References and Related References . (A long list of references, including short descriptions of content of each one.)

• Autumn 2008 FinM 345 Stochastic Calculus, Professor Per Mykland.