MATH 239 Computation and simulation in finance

Instructor:

Isabelle Camilier

camilier at stanford dot edu

Office hours:  Tuesday Thursday 2pm-4:30 pm. Room 383FF

Course Assistant:

Office hours: 

Starting Week 2.

Meeting times: Monday Wednesday 2:15 pm-3:30 pm

Room Art 2

The spring quarter begins on Monday, April 2 and the last lecture is on Wednesday, June 6.

Textbook:

• Monte Carlo Methods in Financial Engineering by Paul Glasserman (Springer). REQUIRED TEXTBOOK.

Other books (OPTIONAL):

• Numerical Solution of Stochastic Differential Equations by Platen and Kloeden (Springer)
• Options, Futures, and Other Derivatives by John Hull

Course grade:

Assignments: 4 homework assignments (30%), due Wednesdays at the beginning of class.

Project: 25%

Final exam: 45% Take home exam due Friday June 8.

It is better to submit a paper version of your assignments. Otherwise please use the dropbox on Coursework.

Prerequisite: MATH 238 or equivalent.

Syllabus:

This course discusses numerical methods for pricing financial derivatives. The emphasis will be on actual implementations and simulations. Monte- Carlo methods, variance reduction, discretization schemes. Finite difference, tree, and transform methods in finance.

Schedule:

	Topics	Comments
Monday April 2	Introduction. Monte Carlo Methods
Wednesday April 4	Monte Carlo Methods. Error analysis.
Monday April 9	Generating random variables
Wednesday April 11	Generating stochastic processes (Brownian motion, Geometric Brownian motion, Ornstein-Uhlenbeck,...)
Monday April 16	Numerical solutions of stochastic differential equations
Wednesday April 18	Numerical solutions of stochastic differential equations (Euler's Scheme, Milstein's scheme...)	HW1 due
Monday April 23	Numerical solutions of stochastic differential equations
Wednesday April 25	Variance reduction techniques (control variates)
Monday April 30	Variance reduction techniques
Wednesday May 2	Variance reduction techniques	HW2 due
Monday May 7	Variance reduction techniques (stratified sampling...)
Wednesday May 9	Computing the Greeks (finite differences)
Monday May 14	Computing the Greeks (advanced methods)
Wednesday May 16	Discrete time methods (European and American options). Binomial, trinomial trees	HW3 due
Monday May 21	Numerical methods for PDEs (discretizing the Black-Scholes PDE)
Wednesday May 23	Numerical methods for PDEs (discretizing the Black-Scholes PDE)
Monday May 28	No classes
Wednesday May 30	Additional topics (rare events)	HW4 due
Monday June 4	Additional topics (quasi-Monte Carlo)	Project due
Wednesday June 6	Review
Friday June 8, 3:15 pm	Final exam (Take home) due