On the Valuation of Currency Options in Stressed Markets

Abstract

The current article handles the valuation of currency options in the market that is suffering from a financial crisis. The standard formulas for this purpose do not perform accurately. European foreign currency exchange options for both the call and the put versions are dealt with. It is assumed that the value of the underlying asset is a stochastic process that follows a modified Black Scholes model with an augmented stochastic volatility to account for the impact of the crisis. Under these settings, a closed form solution is offered for the option-pricing problem on foreign currency. The underlying solution is mathematically proved. In addition, some simulation results and an application are provided. The results based on the new formula accord better with reality compared to the standard formula.