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Date of Award
Spring 2012
Document Type
Restricted Thesis: Campus only access
Degree Name
Bachelor of Science
Department
Mathematics
First Advisor
Dr. Ovidiu Lipan
Abstract
This paper proposes an approach to option valuation, which is based on a generalization of the Fokker-Planck equation (also known as the Kolmogorov forward equation). The Fokker-Planck equation is a truncation of the general Kramers-Moyal (KM) expansion. This expansion has the advantage that it keeps all the coefficients - not merely those related to the drift and the diffusion of the process. Therefore, instead of focusing on the distribution of the underlier assets, one should look at the KM coefficients, as these will carry additional information about the stochastic process followed by the variable in question. By matching the coefficients of the KM expansion of the replicating portfolio - which can be estimated from data - with those of the option, one can get systems of equations for the price of the option. These equations can then be analyzed numerically.
Recommended Citation
Popescu, Dan M., "Option pricing using the Kramers-Moyal expansion" (2012). Honors Theses. 91.
https://scholarship.richmond.edu/honors-theses/91