Approximation and calibration of short-term implied volatility under jump-diffusion stochastic volatility, The review of Financial Studies

We derive a closed-form asymptotic expansion formula for option implied volatility under a two-factor jump-diffusion stochastic volatility model when time-to-maturity is small. Based on numerical experiments we describe the range of time-to-maturity and moneyness for which the approximation is accurate. We further propose a simple calibration procedure of an arbitrary parametric model to short-term near-the-money implied volatilities. An important advantage of our approximation is that it is free of the unobserved spot volatility. Therefore, the model can be calibrated on option data pooled across different calendar dates in order to extract information from the dynamics of the implied volatility smile. An example of calibration to a sample of S&P500 option prices is provided. We find that jumps are significant. The evidence also supports an affine specification for the jump intensity and Constant-Elasticity-of-Variance for the dynamics of the return volatility. Key words: Option pricing, stochastic volatility, asymptotic approximation, jump-diffusion. JEL Classification: G12. 1An early version of this paper has circulated under the title "A simple calibration procedure of stochastic volatility models with jumps by short term asymptotics". We would like to thank the Editor and the referee for constructive criticism and comments which have led to a substantial improvement over the previou