A Study in Hybrid Monte Carlo Methods in Computing Derivative Prices

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.

Name thesis:degree_name

Master of Science (MSc)

Discipline thesis:degree_discipline

Mathematics and Statistics

Grantor dc:publisher.institution

Graduate Studies

Year dc:date.issued

2012

Author dc:creator

• Wang, Binbin

Advisor dc:contributor.advisor

• Ware, Antony

• Economics--Finance
• Mathematics

Statement dc:rights

• University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission.

Language dc:language.iso

eng

DOI

http://dx.doi.org/10.11575/PRISM/25039

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:11023/335