Zhang, Kai, 1983- (2011) Monte Carlo methods in derivative modelling. PhD thesis, University of Warwick.

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Abstract

This thesis addresses issues in discretization and variance reduction methods for Monte Carlo simulation. For the discretization methods, we investigate the convergence properties of various Itˆo-Taylor schemes and the strong Taylor expansion (Siopacha and Teichmann [77]) for the LIBOR market model. We also provide an improvement on the strong Taylor expansion method which produces lower pricing bias. For the variance reduction methods, we have four contributions. Firstly, we formulate a general stochastic volatility model nesting many existing models in the literature. Secondly, we construct a correlation control variate for this model. Thirdly, we apply the model as well as the new control variate to pricing average rate and barrier options. Numerical results demonstrate the improvement over using old control variates alone. Last but not least, with the help of our model and control variate, we explore the variations in barrier option pricing consistent with the implied volatility surface.

Item Type:	Thesis or Dissertation (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Monte Carlo method, Derivative securities -- Mathematical models
Date:	January 2011
Institution:	University of Warwick
Theses Department:	Warwick Business School
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Webber, Nick
Sponsors:	Warwick Business School
Extent:	vi, 218 p. : charts
Language:	eng
URI:	http://wrap.warwick.ac.uk/id/eprint/35689

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