Valuation of Currency Options with Stochastic Interest Rates and Uncertain Exchange Rate

Abstract

There are numerous currency models, but only a few are suitable for practical use. The Liu-Chen-Ralescu (L-C-R) model, proposed by Liu, Chen, and Ralescu, is one of them, where the exchange rate abides by an uncertain differential equation. However, the model treats interest rates as constants, which is unrealistic given the fluctuations in financial markets caused by various human-caused or natural disasters. Our preliminary intention was to explore a model that incorporates additional parameters such as log drift, log diffusion, and variance of the observed data. We discovered a new currency model, referred to as the X-W model, which was proposed by Xiao Wang in his 2019 research article. He proposed that an uncertain differential equation governs the exchange rate, while stochastic differential equations govern both domestic and foreign interest rates. Since the X-W model considers various circumstances and calculates more parameters, the option prices are assumed to be higher. We find the call and put currency option prices for the X-W model using Euler’s method and trapezoidal rule in this article and then the option prices have been compared with the currency option prices obtained from the L-C-R model. Finally, we present some numerical and graphical results for both models using MATLAB coding for better observation. We were successful in finding our expected results and can finally conclude that the X-W model is a better fit for the real market.

J. Bangladesh Math. Soc. 44.2 (2024) 065–076