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APPROXIMATE PRICING OF DERIVATIVES UNDER FRACTIONAL STOCHASTIC VOLATILITY MODEL

Part of: Mathematical finance Stochastic processes

Published online by Cambridge University Press:  15 January 2024

Y. HAN Open the ORCID record for Y. HAN [Opens in a new window]  and
X. ZHENG Open the ORCID record for X. ZHENG [Opens in a new window]
Y. HAN*
Affiliation:
School of Mathematics, Jilin University, Changchun 130012, China; e-mail: [email protected]
X. ZHENG
Affiliation:
School of Mathematics, Jilin University, Changchun 130012, China; e-mail: [email protected]
*
e-mail: [email protected]
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Abstract

This paper examines the issue of derivative pricing within the framework of a fractional stochastic volatility model. We present a deterministic partial differential equation system to derive an approximate expression for the derivative price. The proposed approach allows for the stochastic volatility to be expressed as a composition of deterministic functions of time and a fractional Ornstein–Uhlenbeck process. We apply this method to the European option pricing under the fractional Stein–Stein volatility model, demonstrating its feasibility and reliability through numerical simulations. Our numerical simulations also illustrate the impact of the parameters in the fractional stochastic volatility model on the option price.

Keywords

stochastic volatilityfractional Brownian motionderivatives pricing

MSC classification

Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 65 , Issue 3 , July 2023 , pp. 229 - 247
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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