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OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

Published online by Cambridge University Press:  13 August 2021

Y. HAN
Affiliation:
School of Mathematics, Jilin University, Changchun, 130012,China e-mail: hancy@jlu.edu.cn, lizheng17@mails.jlu.edu.cn
Z. LI
Affiliation:
School of Mathematics, Jilin University, Changchun, 130012,China e-mail: hancy@jlu.edu.cn, lizheng17@mails.jlu.edu.cn
C. LIU*
Affiliation:
School of Mathematics, Jilin University, Changchun, 130012,China e-mail: hancy@jlu.edu.cn, lizheng17@mails.jlu.edu.cn

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.

Type
Research Article
Copyright
© Australian Mathematical Society 2021

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