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

Published online by Cambridge University Press:  23 August 2021

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

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.

Type
Research Article
Copyright
© Australian Mathematical Society 2021

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