#09-04
Exploring Time-Varying Jump Intensities: Evidence from S&P500 Returns and Options
Peter Christoffersen, Kris Jacobs and Chayawat Ornthanalai, November 2008
Abstract: Standard empirical investigations of jump dynamics in returns and volatility are fairly
complicated due to the presence of latent continuous-time factors. We present a new
discrete-time framework that combines heteroskedastic processes with rich specifications
of jumps in returns and volatility. Our models can be estimated with ease using standard
maximum likelihood techniques. We provide a tractable risk neutralization framework
for this class of models which allows for separate modeling of risk premia for the jump
and normal innovations. We anchor our models in the literature by providing continuous
time limits of the models. The models are evaluated by fitting a long sample of S&P500
index returns, and by valuing a large sample of options. We find strong empirical
support for time-varying jump intensities. A model with jump intensity that is affine
in the conditional variance performs particularly well both in return fitting and option
valuation. Our implementation allows for multiple jumps per day, and the data indicate support for this model feature, most notably on Black Monday in October 1987. Our
results also confirm the importance of jump risk premia for option valuation: jumps
cannot significantly improve the performance of option pricing models unless sizeable
jump risk premia are present.
Keywords: compound Poisson process; option valuation; filtering; volatility jumps; jump risk premia; time-varying jump intensity; heteroskedasticity
JEL classifications: G12
