Pricing European stock options using stochastic and fuzzy continuous time processes

Ely, William. Pricing European stock options using stochastic and fuzzy continuous time processes.

Degree: 2012, University of North Carolina – Greensboro

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▼ Over the past 40 years, much of mathematical finance has been built on the premise that stocks tend to move according to continuous-time stochastic processes, particularly geometric Brownian Motion. However, fuzzy set theory has recently been shown to hold promise as a model for financial uncertainty as well, with continuous time fuzzy processes used in place of Brownian Motion. And, like Brownian Motion, fuzzy processes also cannot be measured using a traditional Lebesque integral. This problem was solved on the stochastic side with the development of Ito’s calculus. Likewise, the Liu integral has been developed to measure fuzzy processes. In this paper I will describe and compare the theoretical underpinnings of these models, as well as “back-test” several variations of them on historical market data.; Derivatives, Fuzzy process, Mathematical finance, Stock option Advisors/Committee Members: Jan Rychtar (advisor).
Subjects/Keywords: Stock options – Europe – Mathematical models; Stochastic analysis – Mathematical models; Fuzzy sets – Mathematical models; Brownian motion processes – Mathematical models