A graduate course in the Mathematics in Finance program at the Courarant Institute of Mathematical Sciences of New York University.
Instructor: Professor Jonathan Goodman,
Meeting: Warren Weaver Hall , room 101, Wednesday evenings 5 to 7 pm.
First Class: September 8, 1997
Prerequisites: Scientific Computing, Mathematics of Finance II. This these courses cover basic numerical analysis and mathematical finance. If you have not taken the courses but think you have the background for the course, contact the instructor.
Grading: The grade will be based on weekly assignments, mostly computational.
Course description: Computational techniques for solving mathematical problems arising in finance. Numerical solution of parabolic partial differential equations, basic schemes, general theory, relation to binomial and trinomial trees, boundary conditions for American options, computation of sensitivities, application to one factor and multi factor models. Stochastic simulation and Monte Carlo. Pseudo random number generators, generating random variables with specified distributions, statistical analysis of simulation data and error bars. Numerical solution of stochastic differential equations. Application to pricing, hedging, and portfolio management. Path dependent options. Model calibration and hypothesis testing. Value at risk.
Week 1: Dynamic programming, basic probability and Markov chains, forward and backward inductive computation of probabilities, expected values, and optimal decisions under uncertainty. The notes, in LaTeX format, Postscript format, or HTML, as of September 15. I will try to make the HTML a little better looking soon.
Assignment 1, in postscript format, in LaTeX format, or in HTML (a last resort).
Assignment 2, in postscript format, in LaTeX format, or in HTML.
Assignment 3, in postscript format, in LaTeX format, and (soon) HTML format, along with the data file
Assignment 4, in postscript format, in LaTeX format.
Make sure to check the homework comments and hints page often while doing assignments.
I will be updating the notes from last year and adding new ones as the term progresses. They will be posted here as they become available. Look through the old ones to see what's coming.