Option Pricing Under an Abnormal Economy: using the Square Root of the Brownian Motion

[Purpose] The literature on option pricing is typically suitable to usual circumstances (normal economy). However, in general, under unusual economic states, the traditional models of options are not suitable. Therefore, there is a need to consider alternative stochastic processes and models that captures the unusual states of the economy. [Design/methodology/approach] In this connection, we bridge the gap in the literature by providing a simple, explicit pricing formula for the European option under both normal and abnormal economies. [Findings] In this paper, we first discuss the background theory for the Black-Scholes model under a normal economy when there are no unusual changes in the price of the underlying so that Brownian motion works well. We then provide a simple, explicit pricing formula for the European option under both normal and abnormal economies. This formula is as simple as the classical Black-Scholes formula and there is no need for computational methods. In doing so, we utilize a nontraditional process (the square root of the Brownian motion) and complex analysis. We also rely on a non-traditional stochastic process. Thereafter, we construct three examples to illustrate the use of our proposed model. [Practical implications] The theory developed in this paper is used for investors for their investments and is useful for policy-makers in setting up some rules for the options markets.