## Journal of Econometrics

**Volume 116, Issues 1-2, September-October 2003, Pages 225-257**

J. Econometrics 116 (2003) 225-257

## Alternative models for stock price dynamics

^{a} Mikhail Chernov

^{b} A. Ronald Gallant

^{c} Eric Ghysels

^{d} George Tauchen

^{a}*Columbia Business School, Columbia University*

^{b}*Department of Economics, University of North Carolina*

^{c}*Department of Economics, University of North Carolina*

^{d}*Department of Economics, Duke University*

Received xxxx; revised xxxx; accepted xxxx

**Abstract**

This paper evaluates the role of various volatility specifications,
such as multiple stochastic volatility (SV) factors and jump
components, in appropriate modeling of equity return distributions. We
use estimation technology that facilitates non-nested model
comparisons and use a long data set which provides rich information
about the conditional and unconditional distribution of returns. We
consider two broad families of models: (1) the multifactor loglinear
family, and (2) the affine-jump family. Both classes of models have
attracted much attention in the derivatives and econometrics
literatures. There are various trade-offs in considering such diverse
specifications. If pure diffusion SV models are chosen over jump
diffusions, it has important implications for hedging strategies. If
logarithmic models are chosen over affine ones, it may seriously
complicate option pricing. Comparing many different specifications of
pure diffusion multi-factor models and jump diffusion models, we find
that (1) log linear models have to be extended to 2 factors with
feedback in the mean reverting factor, (2) affine models have to have
a jump in returns, stochastic volatility or probably both. Models (1)
and (2) are observationally equivalent on the data set in hand. In
either (1) or (2) the key is that the volatility can move violently.
As we obtain models with comparable empirical fit, one must make a
choice based on arguments other than statistical goodness of fit
criteria. The considerations include facility to price options, to
hedge and parsimony. The affine specification with jumps in volatility
might therefore be preferred because of the closed-form derivatives
prices.

*JEL Classification*: G13, C14, C52, C53

*Keyword(s)*: Efficient method of moments, Poisson jump
processes, stochastic volatility models