Valuation of Currency Options in Markets with a Crunch

TL;DR

This paper develops a closed-form solution for pricing European currency options in markets experiencing a financial crisis, accounting for stochastic volatility and market stress conditions.

Contribution

It introduces a modified Black-Scholes model with augmented stochastic volatility and derives a closed-form solution for currency option valuation during crises.

Findings

Closed-form pricing formula for currency options under crisis conditions

Simulation results demonstrating model effectiveness

Application to real market data during financial stress

Abstract

This work studies the valuation of currency options in markets suffering from a financial crisis. We consider a European option where the underlying asset is a foreign currency. We assume that the value of the underlying asset is a stochastic process that follows a modified Black-Scholes model with an augmented stochastic volatility. Under these settings, we provide a closed form solution for the option-pricing problem on foreign currency for the European call and put options. A mathematical proof is provided for the underlying solution. In addition, simulation results and an application are provided.