Approximation and Calibration of Short-Term Implied Volatilities Under Jump-Diffusion Stochastic Volatility

We derive an asymptotic expansion formula for option impliedvolatility under a two-factor jump-diffusion stochastic volatilitymodel when time-to-maturity is small. We further propose a simplecalibration procedure of an arbitrary parametric model to short-termnear-the-money implied volatilities. An important advantageof our approximation is that it is free of the unobserved spotvolatility. Therefore, the model can be calibrated on optiondata pooled across different calendar dates to extract informationfrom the dynamics of the implied volatility smile. An exampleof calibration to a sample of S&P 500 option prices is provided.(JEL G12)