GS/MATH 6911 3.0 Numerical Methods in Finance

Summer 2008

Classes: HNE 036 (Thursdays, 19:00-22:00)

Office Hours: Petrie 214, Thursdays, 17:30-18:30

Instructor:Hongmei Zhu

Petrie 214416 736-2100 ext. 55493

Teaching Assistant:Haohan Huang

Ross N507416 736-2100 ext. 40616

Course website:

Evaluation:

ThreeGroup Assignments30% (10% each)

Projects20% (presentation 10%; written report 10%)

Final Exam50% (a three-hour exam)

Important Dates:

May 8First lecture

July 24Last class: project presentations

July 28Project reports due (electronic submission)

July 31Final exam

Mini-Calendar Description

Background materials in partial differential equations: classifications of elliptic, parabolic and hyperbolic equations; examples of exact (closed form) solutions including (that of) the Black-Schole equation and perpetual puts; information flow and propagation [for problems] in finance. Finite difference methods for parabolic equations; explicit methods; implicit methods, including forward and backward Euler methods and Crank-Nicolson method; issues of stability and convergence; applications to finance, including effects of boundary conditions, dividends and transaction costs; degeneracy and exotic options, higher order discretization techniques.

Additional Topics

If time permits, we will also invite two professionals in the financial industry to speak on applications of computational finance. Resumes will be collected a week in advance and be handed to them upon their lectures.

Course Outline (tentative):

  1. Introduction to options and option pricing (1 week).
  2. Lattice methods, deal with time-varying parameters (1 week)
  3. Wiener processes, Ito’s lemma, asset pricing models (1 week)
  4. Generating random numbers and Monte-Carlo simulations(1 week)
  5. Variance reduction methods, quasi Monte-Carlo simulations(1 week)
  6. Black-Scholes equation and PDEs (1 week)
  7. Explicit finite difference method (1 week)
  8. Implicit finite difference method (1 week)
  9. Crank-Nicolson finite difference methods (1 week)
  10. Trading strategies, estimating Greek letters andValue at Risk (1 week)
  11. Other topics in computational finance (2 week)

Textbooks:

[1] Steacie Library2-hr Reservation: P. Brandimarte, Numerical Methods in Finance: A MATLAB-Based Introduction, John Wiley & Sons, Inc., 2002. (HG 176.5 B73 2002; ISBN 0471396869)

[2] Steacie Library2-hr Reservation: John C. Hull, Options, Futures, and Other Derivatives, 6th edition, Prentice Hall, 2005. (HG 6024 A3 H85; ISBN 013149908-4)

References:

[3] Steacie Library 2-hr Reservation: John C. Hull, Student Solution Manual: Options, Futures, and Other Derivatives, 6th edition, 2005. (PCOP.2388 Steacie)

[4]Steacie Library2-hr Reservation: P. Wilmott & P. Brandimarte, Derivatives: the theory and practice of financial Engineering, John Wiley & Sons, Inc, 1998(HG 6024 A3 W557 1998; ISBN 0471983896)

[5] Steacie Library2-hr Reservation: P. Wilmott, J. Dewynne & S. Howison, Option Pricing, Oxford Financial Press, 1993. (HG 6042 W55 1995; ISBN 0952208202)

[6] Steacie Library 2-hr Reservation: B. Daku, MATLAB tutor CD: learning MATLAB superfast! (QA 297 D345 2006, Book & CD ROM)

[7] Steacie Library1-day Reservation: K.W. Morton & D.F. Mayers, Numerical Solution of PDEs, CambridgeUniversity Press, 1994. (ISBN 0521429226)

Assignment & Project Submissions, and Lateness Penalties:

Assignments, project proposal, and final written reports should be submitted at the endof the lectures on their due dates.

Assignments and project reports received later than the due date will bepenalized 50% of the corresponding full grade per day that they are late. Exceptions to thelateness penalty for valid reasons such as illness, compassionate grounds, etc. will beentertained by the Course Director only when supported by written documentation (e.g., adoctor’s letter).

Assignment Marking:

The assignments will consist of programming problems and analytic work.

IMPORTANT: most of the marks for the programming problems will be given for your description of your algorithms (i.e. pseudo-code) and explanation of the results. Simply handing in “raw code”will get very few marks.

Assignment figures and graphs should be carefully thought out to present the data and your conclusionsin an effective and clear manner. Poor presentation of your work will result in a poor mark.

In all cases, I expect you to explain your algorithms, and describe what you see in detail. You shouldalso submit hard copies of your code, along with some documentation. MATLAB has good plottingfacilities. Create figures with MATLAB to include in your assignments.

Important Course Information for Students

All students are expected to familiarize themselves with the following information, available on the Senate Committee on Curriculum & Academic Standards webpage (see Reports, Initiatives, Documents) -

  • York’s Academic Honesty Policy and Procedures/Academic Integrity Website
  • Ethics Review Process for research involving human participants
  • Course requirement accommodation for students with disabilities, including physical, medical, systemic, learning and psychiatric disabilities
  • Student Conduct Standards
  • Religious Observance Accommodation

1