Option Pricing Under The Model With Cross-Feedback Between Self-Exciting Jumps And Volatility

Modeling the asset price reasonably is always one of the research emphases of option pricing,and both volatility and jump are important research objects in asset price model.Recent empirical studies show that the jumps in asset price have the characteristic of self-exciting,which cause the phenomenon of jump clustering.It is especially evident during the financial crisis.Besides,there are jumps in the volatility of asset price,and asymmetric cross-feedback between the volatility and jump of asset price.This paper constructs a new model with cross-feedback between self-exciting jumps and volatility under the framework of affine jump-diffusion,and incorporate the above characteristics of asset price into the model.Base on the model,both the mean processes of the variance and jump intensity of asset price and the conditional characteristic function of asset log-price are derived,and both the semi-analytical option pricing expression and the dynamic optimal hedging position of European call option are obtained.This paper also derives the Greek and the partial derivatives of option price,and analyzes the effects of some parameters in option pricing expression on option price by using numerical simulation.Then,this paper uses the data of SSE 50 ETF call option price to calibrate the model,and analyzes the calibration parameters.The results show that the price of SSE 50 ETF is negatively correlated with its volatility,which means the leverage effect and volatility feedback effect.The price of SSE 50 ETF not only has jump clustering,but also has upward jump clustering and downward jump clustering.There is an asymmetric crossfeedback between the volatility and jump of the price of SSE 50ETF: the effect of downward jump on volatility is greater than the effect of upward jump,and the effect of volatility on downward jump is greater than that on upward jump.Finally,this paper uses the above data to compare and analyze the goodness-of-fit and the predictive abilities of the model proposed by this paper,stochastic volatility double jumps model and Hawkes stochastic volatility jump-diffusion model.The results show that the goodness-of-fit of the model proposed by this paper is better than that of other two models,and the prediction error of the model proposed by this paper is also smaller than that of other two models.Moreover,with the gradually expansion of the prediction time interval,the gaps of the cumulative prediction errors between the model proposed by this paper and other two models are continuously widened,and the relative advantage of the model proposed by this paper in prediction ability will be more obvious.