Risk premiums in a simple market model for implied volatility

Abstract

We incorporate risk premiums for stochastic implied volatility in an arbitrage-free model describing the joint dynamics of options and the security underlying these options. As this model directly describes the implied volatility surface, it also captures dynamics exclusively residing in the option markets. Because an arbitrage-free multi-factor description of the implied volatility surface has yet to be developed, we specify a stochastic implied volatility model with a single factor determining the dynamics of the implied volatility. Parameters in this model are estimated for several markets, and for the S&P 500 the resulting implied volatility risk premium is compared with risk premium estimates from models that describe the instantaneous volatility.