Abstract:
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The purpose of this paper is to shed further light on the tensions that exist between the empiciral fit of stochastic volatility (SV) models and their linkage to option pricing. A number of recent papers have investigated several specifications of one-factor SV diffusion models associated with option pricing models. The empirical failure of one-factor affine, Constant Elasticity of Variance (CEV), and one-factor log-linear SV models leaves us with two strategies to explore: 1.) add a jump component to better fit the tail behavior; or 2.) add an additional (continuous path) factor where one factor controls the persistence in volatility and the second determines the tail behavior. Both have been partially pursued, and our paper embarks on a more comprehensive examination which yields some rather surprising results. Adding a jump component to the basic Heston affine model is known to be a succesful strategy as demonstrated by recent applications. Unfortunately, the presence of a jump component introduces quite a few unpleasant econometric issues. In addition, several financial issues, like hedging and risk factors, become more complex.
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