Markov chains and the pricing of derivatives
Author(s)
Lo, Harry Chung Heng
Type
Thesis
Abstract
A numerical method for pricing financial derivatives based on continuous-time Markov chains
is proposed. It approximates the underlying stochastic process by a continuous-time Markov
chain. We show how to construct a multi-dimensional continuous-time Markov chain such that
it converges in distribution to a multi-dimensional diffusion process. The method is flexible
enough to be applied to a model where the underlying process contains local volatility, stochastic
volatility and jumps. Furthermore, we introduce a method to approximate the dynamics of the
realized variance of a Markov chain and an algorithm to reduce the complexity of computing
the joint probability distribution between the realized variance and the underlying.
is proposed. It approximates the underlying stochastic process by a continuous-time Markov
chain. We show how to construct a multi-dimensional continuous-time Markov chain such that
it converges in distribution to a multi-dimensional diffusion process. The method is flexible
enough to be applied to a model where the underlying process contains local volatility, stochastic
volatility and jumps. Furthermore, we introduce a method to approximate the dynamics of the
realized variance of a Markov chain and an algorithm to reduce the complexity of computing
the joint probability distribution between the realized variance and the underlying.
Date Issued
2009
Date Awarded
2010-01
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Mijatovic, Aleksandar
Creator
Lo, Harry Chung Heng
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)