An analytical option pricing formula for mean-reverting asset with time-dependent parameter

Piyapoom Nonsoong; Khamron Mekchay; Sanae Rujivan

doi:10.21914/anziamj.v63.15172

Authors

Piyapoom Nonsoong Chulalongkorn University https://orcid.org/0000-0002-8791-861X
Khamron Mekchay Chulalongkorn University https://orcid.org/0000-0001-7797-4418
Sanae Rujivan Walailak University https://orcid.org/0000-0002-2755-5263

DOI:

https://doi.org/10.21914/anziamj.v63.15172

Keywords:

option pricing, mean-reverting process, Feynman-Kac formula

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.

doi:10.1017/S1446181121000262

Author Biographies

Piyapoom Nonsoong, Chulalongkorn University

Department of Mathematics and Computer Science, Chulalongkorn University, Bangkok, Thailand.

Khamron Mekchay, Chulalongkorn University

Department of Mathematics and Computer Science, Chulalongkorn University, Bangkok, Thailand.

Sanae Rujivan, Walailak University

Center of Excellence in Data Science for Health Study, Division of Mathematics and Statistics, School of Science, Walailak University, Nakhon Si Thammarat, Thailand.