European and American Option Pricing with a Geometric Markov Renewal Process Underlying Asset Model
Date
2015-02-03
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Abstract
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.
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Keywords
Economics--Finance, Mathematics, Statistics
Citation
Moyer, Z. (2015). European and American Option Pricing with a Geometric Markov Renewal Process Underlying Asset Model (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/25963