A Study in Hybrid Monte Carlo Methods in Computing Derivative Prices
Date
2012-12-05
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Abstract
Hybrid Monte Carlo (HMC) method is defined in this thesis as Monte Carlo method that utilizes conditional expectation so that the
regular Monte Carlo method and other computational methods can be combined to price financial derivatives. This thesis introduces several hybrid Monte Carlo methods and studies the algorithm and
efficiency of these methods, which include three methods combining Monte Carlo with fast Fourier transform, cosine series, and
Black-Scholes formula respectively.
These methods can be considered as ways of variance reduction. The thesis also introduces a new variance reduction method using orthogonal transformation which further reduces the variance. It is shown in this thesis that the HMC methods can significantly improve the efficiency when compared to the regular Monte Carlo method. A
basket option example is used throughout this thesis for implementation and efficiency comparison.
Description
Keywords
Economics--Finance, Mathematics
Citation
Wang, B. (2012). A Study in Hybrid Monte Carlo Methods in Computing Derivative Prices (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25039