Levy Processes in finance

Specialeforsvar ved Simon Gorn Nielsen

Titel:  Levy processes in finance

Abstract: This thesis investigates the properties of the class of stochastic processes called \ly processes, which is a class defined by the property of independent and stationary increments. It turns out that such processes can be decomposed into a continuous part, described by a Brownian motion, and a stochastic jump processes. This makes \ly processes are useful tool in building models of financial assets as they can be used to extend the classical Black-Scholes model in order to better capture the behaviour of financial markets. This thesis focuses on how the special form of the characteristic function of a \ly process can be used to model stock prices and how it is a key component in pricing of for instance call options on this type of underlying asset.

Vejleder:  Thomas Mikosch
Censor:    Søren Asmussen, Aarhus Universitet