Asian Options Pricing and Parameter Estimation of Uncertain Mean-Reverting Currency Model With Exponential Ornstein–Uhlenbeck Exchange Rate

This paper introduces an uncertain mean-reverting currency model that incorporates floating domestic and foreign interest rates along with an exponential Ornstein–Uhlenbeck exchange rate process, all grounded in uncertainty theory. Pricing formulas for both Asian call and put options are derived within this framework. The parameters of the model are estimated using real financial data from Canada and the United States, including the Canadian Overnight Repo Rate Average (CORRA), the American Federal Funds Effective Rate (AFFER), and the monthly average exchange rate of the US Dollar to the Canadian Dollar (USDCAD). The method of moments is applied to estimate the unknown parameters, and goodness-of-fit tests are conducted to validate the parameter estimates. Numerical experiments demonstrate that Asian option prices decrease as domestic and foreign initial interest rates increase. The prices of call and put options show divergent behaviors with respect to the initial exchange rate and the fixed strike price. Additionally, the paper investigates the nonlinear relationship between option prices and expiration time. In the appendix, the uncertain currency model is transformed into a stochastic currency model, and statistical tests confirm its inapplicability to the selected data, thereby substantiating the choice of the uncertain currency model.