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## Applied Analysis: Financial Mathematics

2019-2020
Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

### Doel vak

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.

### Inhoud vak

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.

### Onderwijsvorm

Lectures, exercises, discussion of exercises.

### Toetsvorm

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.

### Literatuur

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.

### Doelgroep

3W, mMath, mBA, 3Ect

### Aanbevolen voorkennis

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

### Algemene informatie

Vakcode X_400076 6 EC P4+5 400 Engels Faculteit der Bètawetenschappen prof. dr. G.J.B. van den Berg prof. dr. G.J.B. van den Berg prof. dr. G.J.B. van den Berg

### Praktische informatie

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