Alternative Models of Stock Prices Dynamics
38 Pages Posted: 31 Jan 2001
Date Written: January 23, 2001
The purpose of this paper is to shed further light on the tensions that exist between the empirical 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 successful strategy as demonstrated by Andersen et al. (1999), Eraker et al. (1999), Chernov et al. (1999), and Pan (1999). 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. In this paper we show that a two-factor log-linear SV diffusion model (without jumps) appears to yield a remarkably good empirical fit. We estimate the model via the EMM procedure of Gallant and Tauchen (1996) which allows us to compare the non-nested log-linear SV diffusion with the affine jump specification. Obviously, there is one drawback to the log-linear SV models when it comes to pricing derivatives since no closed-form solutions are available. Against this cost weights the advantage of avoiding all the complexities involved with jump processes.
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