MATH 239 Computation and simulation in finance

Instructor:

Isabelle Camilier

camilier at stanford dot edu

Office hours:  Monday Wednesday 3:45 pm-5:15 pm in room 383FF.

Room 383FF

 

Course Assistant:

Ka Wai Tsang (ktsang at stanford dot edu).

Office hours:  Tuesday 12-1pm and 2-3pm, Room 207, Sequoia building.

Starting Week 2.

 

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

Room 380 D.

  The spring quarter begins on Monday, April 1. Last day of classes: Wednesday, June 5.

 

Textbook:

Other books (OPTIONAL):

 

Course grade:

Assignments: 4 homework assignments (30%), due Wednesdays (turn in your HW in class, or submit a pdf version using the Coursework dropbox).

Project: 25%. Group presentations in class week 9-10.

Final exam: 45% Take home exam, due Tuesday June 11, 7 pm.

Submit a paper version of your assignments or 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 1 Introduction. Monte Carlo Methods  
Wednesday April 3 Monte Carlo Methods. Error analysis.  
Monday April 8 Generating random variables  
Wednesday April 10 Generating stochastic processes (Brownian motion, Geometric Brownian motion, Ornstein-Uhlenbeck,...) Examples: short rate models.  
Monday April 15 Numerical solutions of stochastic differential equations  
Wednesday April 17 Numerical solutions of stochastic differential equations (Euler's Scheme, Milstein's scheme...) HW1 due
Monday April 22 Variance reduction techniques  
Wednesday April 24 Variance reduction techniques  
Monday April 29 Variance reduction techniques  
Wednesday May 1 Variance reduction techniques HW2 due
Monday May 6 Computing the Greeks (finite differences)  
Wednesday May 8 Computing the Greeks (advanced methods)  
Monday May 13 Discrete time methods (European and American options). Binomial, trinomial trees  
Wednesday May 15 Discrete time methods. HW3 due
Monday May 20 Numerical methods for PDEs (discretizing the Black-Scholes PDE)  
Wednesday May 22 Numerical methods for PDEs (discretizing the Black-Scholes PDE)  
Monday May 27 No classes
Wednesday May 29 Additional topics (rare events) HW4 due
Monday June 3 Presentations  
Wednesday June 5 Presentations  
Tuesday, June 11 Final exam (Take home) due, 7pm.