# American Institute of Mathematical Sciences

October  2019, 15(4): 1921-1936. doi: 10.3934/jimo.2018129

## A mean-reverting currency model with floating interest rates in uncertain environment

 School of Science, Nanjing University of Science and Technology, Nanjing 210094, China

* Corresponding author: Weiwei Wang

Received  March 2018 Revised  April 2018 Published  August 2018

Currency option is an important risk management tool in the foreign exchange market, which has attracted the attention of many researchers. Unlike the classical stochastic theory, we investigate the valuation of currency option under the assumption that the risk factors are described by uncertain processes. Considering the long-term fluctuations of the exchange rate and the changing of the interest rates from time to time, we propose a mean-reverting uncertain currency model with floating interest rates to simulate the foreign exchange market. Subsequently, European and American currency option pricing formulas for the new currency model are derived and some mathematical properties of the formulas are studied. Finally, some numerical algorithms are designed to calculate the prices of these options.

Citation: Weiwei Wang, Ping Chen. A mean-reverting currency model with floating interest rates in uncertain environment. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1921-1936. doi: 10.3934/jimo.2018129
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