Mathematical Sciences

Lund University

  • Title: Pricing of exotic derivatives in the presence of jumps and stochastic volatility
  • Short description:

    In many cases we see that real assets cannot be modeled with reasonable accuracy by Geometric Brownian motions. So we need more complex models to get a good fit to real data. This project
    will deal with techniques to valuate derivatives using such models.

  • Long description:

    In many cases we see that real assets cannot be modeled with reasonable accuracy by Geometric Brownian motions. So we need more complex models to get a good fit to real data. This project
    will deal with techniques to valuate derivatives using such models. Both for simple so called plain vanilla options such as European puts and calls but also for more exotic derivatives such as American options and Barrier options. Depending on your specific field of interest it can be focused in different directions.
    Suggested paths:
    * Simulation based techniques
    * Fourier methods
    * P(I)DE methods

    It is also possible to combine and compare pro and cons of the different methods.

    Literature: Exotic option pricing and advanced Lévy models / edited by Andreas Kyprianou, Wim Schoutens and Paul Wilmott, Chichester : John Wiley, cop. 2005.
    Financial modelling with jump processes / Rama Cont, Peter Tankov
    Boca Raton, Fla. ; London : Chapman & Hall/CRC, cop. 2004
    Available as ebook:http://www.crcnetbase.com/isbn/978-1-58488-413-2

  • Contact: Magnus Wiktorsson