Option pricing for stochastic volatility model with infinite activity Lévy jumps

• Stochastic volatility models and infinite activity Lévy processes are combined.
• The leptokurtosis and heteroskedasticity properties in stock returns are captured.
• Apply intelligent optimization Differential Evolution algorithm to parameters calibration.
• Researches illustrate the superiority of tempered stable distribution in stochastic volatility model.

The purpose of this paper is to apply the stochastic volatility model driven by infinite activity Lévy processes to option pricing which displays infinite activity jumps behaviors and time varying volatility that is consistent with the phenomenon observed in underlying asset dynamics. We specially pay attention to three typical Lévy processes that replace the compound Poisson jumps in Bates model, aiming to capture the leptokurtic feature in asset returns and volatility clustering effect in returns variance. By utilizing the analytical characteristic function and fast Fourier transform technique, the closed form formula of option pricing can be derived. The intelligent global optimization search algorithm called Differential Evolution is introduced into the above highly dimensional models for parameters calibration so as to improve the calibration quality of fitted option models. Finally, we perform empirical researches using both time series data and options data on financial markets to illustrate the effectiveness and superiority of the proposed method.