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 24) considers multilevel Monte Carlo for option pricing in finite activity jumpdiffusion models. We use a jumpadapted Milstein discretisation for constant rate cases and with the thinning method for bounded statedependent rate cases. Multilevel Monte Carlo estimators are constructed for Asian, lookback, 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 αstable 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 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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