Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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THE PRICING OF VULNERABLE FOREIGN EXCHANGE OPTIONS UNDER A MULTISCALE STOCHASTIC VOLATILITY MODEL

  • MIJIN, HA (Department of Mathematics, Pusan National University) ;
  • DONGHYUN, KIM (Department of Mathematics, Pusan National University) ;
  • JI-HUN, YOON (Department of Mathematics, Pusan National University)
  • Received : 2022.04.08
  • Accepted : 2022.10.03
  • Published : 2023.01.30
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Abstract

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

Keywords

Acknowledgement

M. Ha received financial support from the BK21 FOUR Program by the Pusan National University Research Grant, 2021 and the research by J.-H. Yoon was supported by the National Research Foundation of Korea grants funded by the Korean government (NRF-2019R1A2C108931011).

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