Stochastic volatility and stochastic interest rate model with jump and its application on General Electric data

Celep, Betül
In this thesis, we present two different approaches for the stochastic volatility and stochastic interest rate model with jump and analyze the performance of four alternative models. In the first approach, suggested by Scott, the closed form solution for prices on European call stock options are developed by deriving characteristic functions with the help of martingale methods. Here, we study the asset price process and give in detail the derivation of the European call option price process. The second approach, suggested by Bashki-Cao-Chen, describes the closed form solution of European call option by deriving the partial integro-differential equation. In this one we g ive the derivations of both asset price dynamics and the European call option price process. Finally, in the application part of the thesis, we examine the performance of four alternative models using General Electric Stock Option Data. These models are constructed by using the theoretical results of the second approach.


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Contrary to Black-Scholes model in stochastic volatility models, the stock price’s volatility assumed to be a stochastic process and the Brownian motions of volatility and stock price process are correlated with each other. Moreover, in some models, called hybrid stochastic volatility models, the interest rate also assumed to be a stochastic process. Because of the stochastic volatility, stochastic interest rate and correlated Brownian motions, a closed form solution for the Greeks of the options usually do...
Citation Formats
B. Celep, “Stochastic volatility and stochastic interest rate model with jump and its application on General Electric data,” M.S. - Master of Science, Middle East Technical University, 2011.