# An uncertain currency model with floating interest rates

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## Abstract

Considering the uncertain fluctuations in the financial market from time to time, we propose a currency model with floating interest rates within the framework of uncertainty theory. Different from the classical stochastic currency models, this paper is assumed that the domestic interest rate, the foreign interest rate and the exchange rate follow uncertain differential equations. After that, the pricing formulas of European and American currency options are derived. The simulation experiments presented in this paper illustrate the performance of the proposed model, and the relationship between the option pricing formulas and all relevant parameters is analyzed.

## Keywords

Currency model Option pricing formula Floating interest rate Uncertain differential equation## Notes

### Acknowledgments

This work is supported by Natural Science Foundation of Shandong Province (ZR2014GL002).

### Compliance with ethical standards

#### Conflict of interest

The authors declare that they have no conflict of interest to this work.

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