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ANALYTICALLY PRICING EUROPEAN OPTIONS UNDER A TWO-FACTOR STOCHASTIC INTEREST RATE MODEL WITH A STOCHASTIC LONG-RUN EQUILIBRIUM LEVEL

Part of: Mathematical finance

Published online by Cambridge University Press:  19 September 2024

XIN-JIANG HE Open the ORCID record for XIN-JIANG HE [Opens in a new window]  and
SHA LIN Open the ORCID record for SHA LIN [Opens in a new window]
XIN-JIANG HE
Affiliation:
School of Economics, Zhejiang University of Technology, Hangzhou, China; e-mail: [email protected] Institute for Industrial System Modernization, Zhejiang University of Technology, Hangzhou, China
SHA LIN*
Affiliation:
School of Finance, Zhejiang Gongshang University, Hangzhou, China
*
e-mail: [email protected]
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Abstract

We construct a new stochastic interest rate model with two stochastic factors, by introducing a stochastic long-run equilibrium level into the Vasicek interest rate model which follows another Ornstein–Uhlenbeck process. With the interest rate under the Black–Scholes model being assumed to follow the newly proposed model, a closed-form representation of European option prices is successfully presented, when the analytical characteristic function of the underlying log-price under a forward measure is derived. To assess the model performance, a preliminary empirical study is conducted using S&P 500 index and its options, with the Vasicek model and an alternative two-factor Vasicek model taken as benchmarks.

Keywords

two-factor stochastic interest rate modelEuropean optionsclosed-formstochastic long-run equilibrium levelempirical study

MSC classification

Primary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 66 , Issue 2 , April 2024 , pp. 132 - 151
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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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