Math 239 - Computation and Simulation in Finance



Syllabus:
This course discusses numerical methods for pricing financial derivatives. The emphasis will be on actual implementations and simulations. In doing so, this course aims at a broader understanding of financial derivatives (exotics, early exercise,...), of stochastic processes (Itô's formula, SDE, Girsanov's tranform,...), and of PDE (convergence and stability for numerical schemes).

Prerequisite: 238 and some programming experience.


Meetings: Mon Wed Fri 03:15 - 04:05, Room 380-380X

Instructor: Valdo Durrleman
Office hours: Thursday 1:00 - 3:00, or by appointment, Room 382-K

Course Assistant: Manuel Zamfir (zamfir "at" math.stanford.edu)
Office hours: Monday 1:15 - 3:15, Tuesday and Thursday 9:00 - 11:00, Room 380-H

Texts: All optionals, all will be on reserve at the Math/CS library. The first two focus on computational issues; the last two are broader in scope but also contain discussions about numerics.
Monte Carlo Methods in Financial Engineering, by Glasserman (Springer Verlag, 2003)
Implementing Derivatives Models, by Clewlow and Strickland (Wiley and Sons, 1998)
Mathematics of Financial Derivatives: A Student Introduction, by Wilmott, Dewynne, and Howison (Cambridge University Press, 1995)
Options, Futures, and Other Derivatives, 5th ed, by Hull (Prentice Hall, 2003)

Outline:
Week of April 2: Review of Itô's calculus and the classical Black-Scholes-Merton theory
Week of April 9: Prices as expectations, introduction to Monte Carlo methods, error analysis
Week of April 16: Simulation (random variables, stochastic processes, SDE, Milstein's scheme)
Week of April 23: Variance reduction techniques, Greeks
Week of April 30: Exotics
Week of May 7: Binomial/Trinomial trees
Week of May 14: Implied trees, American options
Week of May 21: Finite differences
Week of May 28: Linear complementarity problems

Assignments: There will be 5 homework assignments (look under course materials), each involving coding.
HW1 (due on Wednesday, April 18)
HW2 (due on Friday, April 27)
HW3 (due on Wednesday, May 9)
HW4 (due on Monday, May 21)
HW5 (due on Wednesday, June 6)

Matlab Resources:
Documentation at Mathworks

Matlab Primer by Kermit Sigmon

To run the Matlab GUI on Leland systems remotely from your Windows machine, download and install a demo copy of X-Win32.
Whenever you want to run Matlab remotely, start X-Win32.
From a Leland prompt type "setenv DISPLAY xxx.xxx.xxx.xxx:0", where the xxx's stand for your Windows machine's IP address.
Alternatively, you can use a name instead of an IP. For example, if the name by which you registered your PC with Stanford is "mojo",
type "setenv DISPLAY mojo.stanford.edu:0"
Then from the Leland prompt, type "matlab &" to start Matlab.
Then type "xterm &" to open up an X terminal, from which you can start your favorite text editor.
After 30 days the demo will be crippled.