Skewness and option prices under stochastic volatility models: the role of shot-noise jumps

In this paper, we propose a novel option pricing model that incorporates both shot-noise effects in stock return jumps and stochastic volatility. The model aims to reflect the decaying effects on stock returns after the shock and attempts to provide a more reasonable structure for return jumps. We emphasize the theoretical nature of this paper and manage to derive closed-form expressions for the VIX index and the SKEW index under the new model. For the VIX index, we prove that it can be decomposed into a linear combination of the volatility part and the jump part. For the SKEW index, we obtain its analytical representation beyond traditional affine models and check its sensitivity with respect to model parameters. We also perform a calibration exercise using options data to compare our model with a classical stochastic volatility model with jumps. Several empirical observations are made.