Efficient pricing and hedging under the double Heston stochastic volatility jump-diffusion model

The performances of jump-risk mitigation under a double Heston stochastic volatility jump-diffusion dbHJ model are examined. The quadratic exponential QE scheme is used to simulate the -measure price paths supposed to follow the dbHJ model, whereas a Fourier-COS-expansion-based scheme i.e. the COS formula, see [F. Fang and C.W. Oosterlee, A novel pricing method for European based on Fourier-cosine series expansions, SIAM J. Sci. Comput. 31 2008, pp. 826–848] is employed to price options and to calculate Greeks. Numerical results from extensive dynamic hedging experiments suggest that, when facing a -measure market with stiff volatility skews and non-trivial jumps, the dbHJ model is better than the plain double Heston and Black–Scholes models, and slightly outperforms the Heston stochastic volatility jump-diffusion HJ model and the Merton model in mitigating the jump risk of an option. This conclusion holds independent of the model specification of -measure market.