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AN ANALYTICAL OPTION PRICING FORMULA FOR MEAN-REVERTING ASSET WITH TIME-DEPENDENT PARAMETER

Part of: Equations of mathematical physics and other areas of application Mathematical finance

Published online by Cambridge University Press:  23 August 2021

P. NONSOONG Open the ORCID record for P. NONSOONG [Opens in a new window] ,
K. MEKCHAY Open the ORCID record for K. MEKCHAY [Opens in a new window]  and
S. RUJIVAN Open the ORCID record for S. RUJIVAN [Opens in a new window]
P. NONSOONG
Affiliation:
Department of Mathematics and Computer Science, Chulalongkorn University, Bangkok, Thailand; e-mail: piyapoom.n@hotmail.com
K. MEKCHAY*
Affiliation:
Department of Mathematics and Computer Science, Chulalongkorn University, Bangkok, Thailand; e-mail: piyapoom.n@hotmail.com
S. RUJIVAN
Affiliation:
Center of Excellence in Data Science for Health Study, Division of Mathematics and Statistics, School of Science, Walailak University, Nakhon Si Thammarat, Thailand; e-mail: rsanae@wu.ac.th
*
e-mail: khamron.m@chula.ac.th
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Abstract

We present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided.

Keywords

option pricingmean-reverting processFeynman–Kac formula

MSC classification

Primary: 91G20: Derivative securities
Secondary: 35Q91: PDEs in connection with game theory, economics, social and behavioral sciences
Type
Research Article
Information
The ANZIAM Journal , Volume 63 , Issue 2 , April 2021 , pp. 178 - 202
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Copyright
© Australian Mathematical Society 2021

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