Document Type thesis Author Name shen, karl URN etd-042909-150321 Title A Preliminary View of Calculating Call Option Prices Utilizing Stochastic Volatility Models Degree MS Department Mathematical Sciences Advisors Hasanjan Sayit, Advisor Bogdan Vernescu, Department Head Keywords Option Pricing Stochastic volatility CIR Model Date of Presentation/Defense 2009-05-05 Availability unrestricted
We will begin with a review of key financial topics and outline many of the crucial ideas utilized in the latter half of the paper. Formal notation for important variables will also be established. Then, a derivation of the Black-Scholes equation will lead to a discussion of its shortcomings, and the introduction of stochastic volatility models. Chapter 2 will focus on a variation of the CIR Model using stock price in the volatility driving process, and its behavior to a greater degree. The key area of discussion will be to approximate a hedging function for European call option prices by Taylor Expansion. We will apply this estimation to real data, and analyze the behavior of the price correction. Then make conclusions about whether stock price has any positive effects on the model.
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