Option Pricing and Parameter Estimation for Uncertain Mean-Reverting Currency Model

Option pricing problem is one of the significant issues in the foreign exchange market, which has attracted the attentions of many researchers. Unlike the classical stochastic theory, we investigate option pricing by an uncertain currency model under the foundation of uncertainty theory. By considering that the domestic interest rate, the foreign interest rate and exchange rate have long-term fluctuations, this paper mainly introduces the uncertain mean-reverting currency model, and conducts the pricing formula of European call options and American call options. Furthermore, the moment methods would be applied to estimating all unknown parameters of the currency model by using Australian Interbank Overnight Cash Rate, US Federal Funds Effective Rate and their Exchange Rate (ExR). Moreover, this paper takes the Goodness-of-Fit Test on whether the moment estimates are acceptable. Finally, the numerical examples and algorithms are used to calculate the option prices and to illustrate the relationship between the two prices and the relationship between prices and their parameters. The appendix justifies our preference for the uncertain currency model over the stochastic one for forex market analysis, based on the latter’s superior fit to empirical data.