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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