Financiële stochastiek
2001-2002


Inhoud

In dit college komen wat geavanceerdere onderwerpen uit de financiele stochastiek dan de Black-Scholes problematiek aan de orde. Hieronder vallen onder meer het waarderen van Amerikaanse call en put opties en Aziatische opties en rentemodellen (Heath-Jarrow-Morton. In het begin van het college worden essentiele delen van martingaaltheorie en stochastische integratie samengevat. Enige vertrouwdheid met de beginselen van stochastische calculus wordt echter bekend verondersteld, bijvoorbeeld zoals die behandeld wordt in het college Brownse beweging en stochastische integralen.

Contents

In this course we present topics from financial stochastics, including derivative pricing, (Black-Scholes and exotic products like American style options, Asian options) and interest models (Heath-Jarrow-Morton), which are the basis of the "financial engineering" by modern financial institutions. We consider these topics in continuous time, using diffusion models for the financial processes. The course will start with a review of the theory of martingales and stochastic integration, but is meant for students who are already somewhat familiar with these subjects. (For instance, from the course on Brownian motion and stochastic integration given at the UvA in the first trimester.)
 

Schedule

2nd trimester, Wednesdays 15-17 in room P.016, Thursdays 11-13 in room P.015A (Universiteit van Amsterdam, Plantage Muidergracht 24)
 

Docenten

A.W. van der Vaart (VU) en P.J.C. Spreij (UvA)
 

Literature

The course is based on parts of:

T. Bjork, Arbitrage theory in continuous time
M. Musiela & M. Rutkowski, Martingale Methods in Financial Modelling
P.J. Hunt & J.E. Kennedy, Financial Derivatives in Theory and Practice (HK)
Ioannis Karatzas and Steve Shreve, Methods of Mathematical Finance

There is a detailed list of the treated subjects.
 

Homework

Exercises for weeks 1, 2, 3, 7 and 8 are available in ps and in pdf.

The exercises for the weeks 4, 5, 6, 9 and 10 can be found as a ps file at the companion page.
 
 

Participants

Programme

Week 1  Class: HK pages 19-42
Homework: 5 exercises from "Week 1"
Week 2 Class: HK pages 42-72
Homework: 6 exercises from "Week 2"
Week 3 Class: HK pages 74-94
Homework: 5 exercises from "Week 3"
Week 4 See companion page
Week 5 See companion page
Week 6 See companion page
Week 7 Class: HK pages 183-202
Homework: "Week 7"
Week 8 Class: HK pages 202-210, 319-323, 325-328
Homework: 4 exercises from "Week 8"
Week 9 See companion page
Week 10
See companion page