# 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
##### References:

show all references

##### References:
 [1] Xiao-Qian Jiang, Lun-Chuan Zhang. A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 969-978. doi: 10.3934/dcdss.2019065 [2] Cuilian You, Le Bo. Option pricing formulas for generalized fuzzy stock model. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-10. doi: 10.3934/jimo.2018158 [3] Xu Chen, Jianping Wan. Integro-differential equations for foreign currency option prices in exponential Lévy models. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 529-537. doi: 10.3934/dcdsb.2007.8.529 [4] Frederic Abergel, Remi Tachet. A nonlinear partial integro-differential equation from mathematical finance. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 907-917. doi: 10.3934/dcds.2010.27.907 [5] Fazlollah Soleymani, Ali Akgül. European option valuation under the Bates PIDE in finance: A numerical implementation of the Gaussian scheme. Discrete & Continuous Dynamical Systems - S, 2018, 0 (0) : 889-909. doi: 10.3934/dcdss.2020052 [6] Kai Zhang, Song Wang. Convergence property of an interior penalty approach to pricing American option. Journal of Industrial & Management Optimization, 2011, 7 (2) : 435-447. doi: 10.3934/jimo.2011.7.435 [7] Kun Fan, Yang Shen, Tak Kuen Siu, Rongming Wang. On a Markov chain approximation method for option pricing with regime switching. Journal of Industrial & Management Optimization, 2016, 12 (2) : 529-541. doi: 10.3934/jimo.2016.12.529 [8] Tak Kuen Siu, Howell Tong, Hailiang Yang. Option pricing under threshold autoregressive models by threshold Esscher transform. Journal of Industrial & Management Optimization, 2006, 2 (2) : 177-197. doi: 10.3934/jimo.2006.2.177 [9] Kai Zhang, Xiaoqi Yang, Kok Lay Teo. A power penalty approach to american option pricing with jump diffusion processes. Journal of Industrial & Management Optimization, 2008, 4 (4) : 783-799. doi: 10.3934/jimo.2008.4.783 [10] Zhuo Jin, Linyi Qian. Lookback option pricing for regime-switching jump diffusion models. Mathematical Control & Related Fields, 2015, 5 (2) : 237-258. doi: 10.3934/mcrf.2015.5.237 [11] Nan Li, Song Wang. Pricing options on investment project expansions under commodity price uncertainty. Journal of Industrial & Management Optimization, 2019, 15 (1) : 261-273. doi: 10.3934/jimo.2018042 [12] Avner Friedman, Harsh Vardhan Jain. A partial differential equation model of metastasized prostatic cancer. Mathematical Biosciences & Engineering, 2013, 10 (3) : 591-608. doi: 10.3934/mbe.2013.10.591 [13] Wenjia Jing, Olivier Pinaud. A backscattering model based on corrector theory of homogenization for the random Helmholtz equation. Discrete & Continuous Dynamical Systems - B, 2019, 24 (10) : 5377-5407. doi: 10.3934/dcdsb.2019063 [14] Yeming Dai, Yan Gao, Hongwei Gao, Hongbo Zhu, Lu Li. A real-time pricing scheme considering load uncertainty and price competition in smart grid market. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-17. doi: 10.3934/jimo.2018178 [15] María Suárez-Taboada, Carlos Vázquez. Numerical methods for PDE models related to pricing and expected lifetime of an extraction project under uncertainty. Discrete & Continuous Dynamical Systems - B, 2019, 24 (8) : 3503-3523. doi: 10.3934/dcdsb.2018254 [16] Xiaohong Chen, Kui Li, Fuqiang Wang, Xihua Li. Optimal production, pricing and government subsidy policies for a closed loop supply chain with uncertain returns. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-26. doi: 10.3934/jimo.2019008 [17] Dejian Chang, Zhen Wu. Stochastic maximum principle for non-zero sum differential games of FBSDEs with impulse controls and its application to finance. Journal of Industrial & Management Optimization, 2015, 11 (1) : 27-40. doi: 10.3934/jimo.2015.11.27 [18] Alberto A. Pinto, Telmo Parreira. Localization and prices in the quadratic Hotelling model with uncertainty. Journal of Dynamics & Games, 2016, 3 (2) : 121-142. doi: 10.3934/jdg.2016006 [19] Alex Capaldi, Samuel Behrend, Benjamin Berman, Jason Smith, Justin Wright, Alun L. Lloyd. Parameter estimation and uncertainty quantification for an epidemic model. Mathematical Biosciences & Engineering, 2012, 9 (3) : 553-576. doi: 10.3934/mbe.2012.9.553 [20] Xiangfeng Yang, Yaodong Ni. Extreme values problem of uncertain heat equation. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1995-2008. doi: 10.3934/jimo.2018133

2018 Impact Factor: 1.025