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OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

Part of: Mathematical finance Stochastic processes

Published online by Cambridge University Press:  13 August 2021

Y. HAN Open the ORCID record for Y. HAN [Opens in a new window] ,
Z. LI Open the ORCID record for Z. LI [Opens in a new window]  and
C. LIU Open the ORCID record for C. LIU [Opens in a new window]
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
*
e-mail: liucy17@mails.jlu.edu.cn
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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.

Keywords

fractional Brownian motionstochastic volatilityMalliavin calculusoption pricing

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 2 , April 2021 , pp. 123 - 142
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Copyright
© Australian Mathematical Society 2021

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