Option Pricing under Double Heston Model with Approximative Fractional Stochastic Volatility

Abstract

We establish double Heston model with approximative fractional stochastic volatility in this article. Since approximative fractional Brownian motion is a better choice compared with Brownian motion in financial studies, we introduce it to double Heston model by modeling the dynamics of the stock price and one factor of the variance with approximative fractional process and it is our contribution to the article. We use the technique of Radon–Nikodym derivative to obtain the semianalytical pricing formula for the call options and derive the characteristic functions. We do the calibration to estimate the parameters. The calibration demonstrates that the model provides the best performance among the three models. The numerical result demonstrates that the model has better performance than the double Heston model in fitting with the market implied volatilities for different maturities. The model has a better fit to the market implied volatilities for long-term options than for short-term options. We also examine the impact of the positive approximation factor and the long-memory parameter on the call option prices.

Valuation of Insurance Products with Shout Options in a Jump-Diffusion Model

“…Among these, the jump-diffusion model described more accurately than a Brownian motion [14][15][16][17][18][19][20]. Moreover, some models for describing the underlying asset were the stochastic volatility jump model [21,22], the double stochastic volatility model with jumps [23,24], etc. e objective of this article is to propose a new mathematical model that can be used to value insurance products with shout options, while making an assumption about a jump-diffusion model followed by the underlying asset.…”