Course Objective

After completion of the course, the student can:

1. explain the payoff function of several options and use a no-arbitrage
argument to explain relations between several standard options,

2. use the binomial model for option pricing, including replicating
portfolio's,

3. understand the stochastic model for the share process and how that
leads to the Black-Scholes equation,

4. describe solutions of some partial differential equations, in
particular linear parabolic pde's, depending on boundary and initial
conditions,

5. discuss American options and the relation to free boundary problems,

6. apply finite difference methods for the solution of the heat equation
and associated stability issues.

Course Content

This course gives an introduction to financial mathematics.
The following subjects will be treated:
- introduction in the theory of options;
- the binomial method;
- introduction to partial differential equations;
- the heat equation;
- the Black-Scholes formula and applications;
- introduction to numerical methods, approximating the price of an
(American) option.

Teaching Methods

Lectures, exercises, discussion of exercises.

Method of Assessment

There will be sets of homework (at least 4) which will count for 40
percent of the total grade, and a final written exam which will count
for 60 percent. There is a resit for the final exam. A grade of 5.0 for
the final exam is required to pass the course. The homework still counts
for the resit exam.

Literature

The Mathematics of Financial Derivatives, A Student Introduction, by
Paul Wilmott, Sam Howison, Jeff Dewynne. Cambridge University Press.

In addition, lecture notes will be made available.

Target Audience

3W, mMath, mBA, 3Ect

Recommended background knowledge

Single Variable and Multivariable Calculus, Linear Algebra and
Probability Theory as in the VU courses on these subjects