ANNOUNCEMENT: The Friday lectures have been re-scheduled to other lecture rooms. On September 16 we shall be in C 147. The new rooms are listed in the current version of the "rooster".

number of credit points: 6

This course gives an introduction into
financial mathematics. The emphasis is on analysis, although
the first few weeks a more stochastic approach is sketched.
For the latter part we use the book: Financial Calculus, An
introduction to derivative pricing, by Martin Baxter and
Andrew Rennie (Cambridge University Press, Cambridge, 1996),
out of which we treat the first two chapters.
The rest of the course is based on the book The Mathematics of
Financial Derivatives, A student introduction, by
P. Wilmott, S. Howison, and J. Dewynne (Cambridge Unversity
Press, 1995). Out of this book we treat at least chapters 1,
2, 3, 4, 5, 7, 8, 9. The student should also read chapter 10.

The following topics are treated:

- introduction to the theory of options
- binomial tree model;
- introduction to Ito-calculus;
- the Black-Scholes model;
- the classical partial differential equations;
- the Black-Scholes formula with applications;
- American options and free boundary problems;
- introduction to numerical methods for pde's based on applications in financial mathematics.

Course schedule and grading

Lectures will be on Tuesday (15.30-17.15) and
Friday (11.00-12.30) for the first seven weeks. Please check the schedule
for the locations.
There will be homework to be
handed in, this counts towards the grade. There will be a
final oral examination.

literature

- Martin Baxter en Andrew Rennie: Financial Calculus, An introduction to derivative pricing, (Cambridge University Press, Cambridge, 1996)
- P. Wilmott, S. Howison, en J. Dewynne: The Mathematics of Financial Derivatives, A student introduction, (Cambridge Unversity Press, 1995)

Prerequisites:

Calculus, Probability Theory and Analysis.

Intended audience: 3W, 3 Ectr, Master BMI, Master Mathematics, Master SFM.

- Email address: ran AT cs.vu.nl

Room: R3.45

telephone: 020 5987691

First homework. Read Chapter 1 of the book by Wilmott et al.
Produce and hand in a plot containing the payoff diagram (as a
function of exercise price, and for a fixed share price) of an
option (either call or put), combined with option prices.
(Compare the graph in the book, or the graphs produced in class.)
You have to be explicit about the source of your data, and about
what the graph actually shows.

The deadline for this is Tuesday, September 20.

Second homework. This is available as a pdf file: click here to download.

Third set of exercises: from Wilmott et al., Chapter 2, exercises 1, 3, and 5.

Fourth set of exercises: from Wilmott et al. Chapter 3, exercises 2b, d, 3, and 6.
The deadline for this set of homeworks is Friday November 4.

A pdf file for the lecture on separation of variables for the heat equation on a finite interval is available by clicking here .