An empirical testing of a jump-diffusion pricing model with stochastic volatility

                         Arnold, Thomas More; PhD

                         UNIVERSITY OF GEORGIA, 1998

                         ECONOMICS, FINANCE (0508); ECONOMICS, THEORY (0511)

                         The inability of the Black-Scholes Model (1973) to price options of the same maturity across moneyness
                         assuming a constant volatility parameter is known as strike price bias or the volatility smile. This thesis
                         investigates the potential mitigation of strike price bias by option pricing models that allow stochastic
                         volatility and Poisson jumps. A stochastic volatility model with a jump process (SVJ) is estimated using
                         Hansen's Generalized Method of Moments (1982). A second model is estimated excluding the jump
                         process (SV). Both models are estimated using Standard and Poors' 500 Index Option (SPX) data
                         between 1987 and 1991 and then estimated again using the same data excluding the year 1987. 10 to
                         38 day and 38 to 129 day SPX options are used in the estimation. Statistical testing over the estimation
                         period demonstrates that both models under either set of parameter estimates conform to the data.
                         Further testing shows that restricting the SVJ model to a SV model is not statistically feasible. Thus, both
                         models can be viewed as separate entities. Individual parameter testing demonstrates that the SVJ
                         model favors the jump parameters as an explanation for volatility. However, some stochastic volatility
                         parameters remain significant and all stochastic volatility parameters become significant when the jump
                         process is removed. Further analysis into the strike price bias shows that it is not completely eliminated.
                         Absolute average pricing errors and mean squared pricing errors are calculated for the SVJ, SV, and B-S
                         models. For the shorter term options, there is no economically significant difference in performance
                         between the SV and SVJ models. However, the SVJ model performs the best for longer term options in
                         an economically significant manner. To further test strike price bias the parameter estimates are used to
                         price SPX options from 1992 through 1995. The analysis of the strike price bias is considered an
                         out-of-sample testing of the models. The SVJ model performs well at first, but begins to falter outside of
                         1992. The SV model performs well for away from the money options, but at the cost of mispricing near
                         the money options.


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