Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility

Ying Chang,Sumei Zhang,Yiming Wang

doi:10.3390/math9020126

Ying Chang, Sumei Zhang + Show 1 more

Open Access

https://doi.org/10.3390/math9020126

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Abstract

Based on the present studies about the application of approximative fractional Brownian motion in the European option pricing models, our goal in the article is that we adopt the creative model by adding approximative fractional stochastic volatility to double Heston model with jumps since approximative fractional Brownian motion is more proper for application than Brownian motion in building option pricing models based on financial market data. We are the first to adopt the creative model. We derive the pricing formula for the options and the formula for the characteristic function. We also estimate the parameters with the loss function for the model and two nested models and compare the performance among those models based on the market data. The outcome illustrates that the model offers the best performance among the three models. It demonstrates that approximative fractional Brownian motion is more proper for application than Brownian motion.

Highlights

We aim to derive European option pricing formula under the framework of double Heston model including approximative fractional stochastic volatility and jumps
The model has advantages of mean-reverting and non-negative characteristics. Another advantage of the model is that it only needs to explore the characteristic functions for obtaining the pricing formula for the options
Approximative fractional Brownian motion has been used in building stochastic volatility models in recent years

Summary

Introduction

We aim to derive European option pricing formula under the framework of double Heston model including approximative fractional stochastic volatility and jumps. Ahlip et al [15] developed an option pricing model under the framework of the forward stock price They adopted expectation method to derive the characteristic functions. Sattayatham and Intarasit [29] developed a model by adopting an approximation of fractional stochastic volatility model with jumps They derived pricing formula for the options. Some authors developed option pricing model with approximative fractional Brownian motion under a creative framework. In consideration of the present studies, we adopt a double Heston model with approximative fractional stochastic volatility and jumps. Our innovation in the article is that we adopt this creative model by adding approximative fractional stochastic volatility to double Heston model with jumps since no one has developed this model before.

The Model

The Characteristic Function

Calibration

Conclusions