A novel jump diffusion model based on SGT distribution and its applications

Abstract

In this study, we propose two novel jump diffusion models, named the BS-SGT model and the Kou-SGT model, to characterize the asymmetric return distribution with skewness, excess kurtosis, and heavy tails. The two models are based on two existing initial models (the Black-Scholes (BS) model and the Kou's jump diffusion model) respectively by introducing a skewed generalized t distribution (SGT). Moreover, we use the bipower variation test and the maximum likelihood estimation method to prove the existence of jumps and estimate parameters, respectively. Further, several GARCH family models with some compound return distributions are presented to compare with the above novel jump diffusion models on the volatility forecast performance. Two main conclusions are as follows. First, for the asset return distribution describing performance, the results of empirical analysis show that the novel jump diffusion model is more tractable to handle and capture the characteristics of the asymmetric distribution with skewness, excess kurtosis, and heavy tails than the corresponding initial model in financial market. Second, the models with SGT distribution forecast volatility more accurately than the corresponding models without SGT distribution. In addition, the GARCH family models with compound return distribution outperform the corresponding jump diffusion models.