Closed-form implied volatility surfaces for stochastic volatility models with jumps

We develop a closed-form bivariate expansion of the shape characteristics of the implied volatility surface generated by a stochastic volatility model with jumps in returns. We use the expansion to analyse the impact on the shape of the implied volatility surface of the various features of the stochastic volatility model and to determine which stochastic volatility models are capable of reproducing the observed characteristics of the implied volatility market data.