Option pricing under the fractional stochastic volatility model

Authors

DOI:

https://doi.org/10.21914/anziamj.v63.15204

Keywords:

fractional Brownian motion , stochastic volatility, Malliavin calculus, option pricing

Abstract

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented.

doi:10.1017/S1446181121000225

Author Biographies

Yuecai Han, Jilin University

School of Mathematics, Jilin University, Changchun, China.

Zheng Li, Jilin University

School of Mathematics, Jilin University, Changchun, China.

Chunyang Liu, Jilin University

School of Mathematics, Jilin University, Changchun, China.

 

Published

2021-10-02

Issue

Section

Special Issue for Financial Mathematics, Probability and Statistics