The Mathematical Institute, University of Oxford, Eprints Archive

Multilevel Monte Carlo for jump processes

Xia, Yuan (2013) Multilevel Monte Carlo for jump processes. PhD thesis, University of Oxford.

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Abstract

This thesis consists of two parts. The first part (Chapters 2-4) considers multilevel Monte Carlo for option pricing in finite activity jump-diffusion models. We use a jump-adapted Milstein discretisation for constant rate cases and with the thinning method for bounded state-dependent rate cases. Multilevel Monte Carlo estimators are constructed for Asian, look-back, barrier and digital options. The computational efficiency is numerically demonstrated and analytically justified.

The second part (Chapter 5) deals with option pricing problems in exponential Levy models where the increments of the underlying process can be directly simulated. We discuss several examples: Variance Gamma, Normal Inverse Gaussian and α-stable processes and present numerical experiments of multilevel Monte Carlo for Asian, lookback, barrier options, where the running maximum of the Levy process involved in lookback and barrier payoffs is approximated using discretely monitored maximum. To analytically verify the computational complexity of multilevel method, we also prove some upper bounds on $L^p$ convergence rate of discretely monitored error for a broad class of Levy processes.

Item Type:Thesis (PhD)
Subjects:O - Z > Probability theory and stochastic processes
H - N > Numerical analysis
Research Groups:Mathematical and Computational Finance Group
ID Code:1831
Deposited By: Eprints Administrator
Deposited On:19 Apr 2014 09:24
Last Modified:29 May 2015 19:31

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