Stochastic volatility double-jump-diffusions model: the importance of distribution type of jump amplitude

This research examines whether there exists an appealing distribution for random jump amplitude, in the sense that with which the stochastic volatility double-jump-diffusions (SVJJ) model would potentially have a superior option market fit, meanwhile keeping a sound balance between reality and tractability. We provide a general methodology for pricing vanilla options, using the Fourier cosine series expansion method (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], in the setting of Heston's SVJJ (HSVJJ) model that may allow a range of jump amplitude distributions, including the normal distribution, the exponential distribution and the asymmetric double-exponential (db-E) distribution as special cases. An illustrative example examines the implications of HSVJJ model in capturing option ‘smirks’. This example highlights the impacts on implied volatility surface of various jump amplitude distributions, through both extensive model calibrations and implied-volatility impacting experiments. Numerical results show that, with the db-E distribution, the HSVJJ model not only captures the implied volatility smile and smirk, but also the ‘sadness’.