Derivation of European Option Pricing Formula when the Asset is Geometric Mean Reverting

Abstract

An option is a financial tool with the potential to increase profitability and dynamically contribute to effective ways of managing funds and mitigating risk in the financial sector. The evolution of options by Black-Scholes since its inception has played a vital role in improving the economy, hence the essence of valuation techniques that determine the option price. Geometric Brownian motion was commonly used to describe the behaviour of an asset price, as it may be, other assets exhibit a mean-reverting process. The pricing formula has been derived for assets that follow the geometric Brownian motion model only but in this article, we derived a pricing formula for a European option for an asset that follows a geometric mean-reverting model. We then compared it to a Monte Carlo Simulation technique to price the European option. The two methods gave close valuations but with regards to the time efficiency of the two methods, the derived formula was less. Also, the mean absolute error between the two methods was 0.0177 for the European put options; while, the mean absolute error between the two methods for the European call options was 0.0434. Also, from our analysis, when pricing a European option for this kind of asset, it is better to take note of the interest rate and how volatile it is in the market and that will inform the choice of option to trade.