European and American Option Pricing with a Geometric Markov Renewal Process Underlying Asset Model

We present methods for pricing of American and European options under a Geometric Markov Renewal Process (GMRP) as the underlying asset model. We provide a detailed overview of the GMRP. Discussions of Markov processes, Geometric Brownian Motion, and GMRP approximation techniques are presented. We discuss the Aase trading model, with a MATLAB implementation. We discuss the Black-Scholes and binomial Cox-Ross-Rubinstein formulas for European and American options. We present results on Fixed Time Increments GMRP, with a derivation of a method for a limiting case of Fixed Time Increments GMRP (applicable to perpetual American options), complete with MATLAB implementations. We also present a MATLAB implementation for the pricing of European options under GMRP with an arbitrary jump distribution. We discuss diffusion and normal deviated approximations of a GMRP, and present MATLAB implementations for pricing American and European options. We follow this with a discussion of a Poisson approximation of a security market. A literature review is presented, together with an appendix including our MATLAB implementations. Conclusions and recommendations for future research directions conclude the paper.

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

2015

Author dc:creator

• Moyer, Zachary

Advisor dc:contributor.advisor

• Swishchuk, Anatoliy

• Economics--Finance
• Mathematics
• Statistics

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/25963

OAI identifier oai:identifier

oai:ucalgary.scholaris.ca:11023/2074