Pricing formula for European currency option and exchange option in a generalized jump mixed fractional Brownian motion with time-varying coefficients

Kyong-Hui Kim, Sim Yun, Nam-Ung Kim and Ju-Hyuang Ri

Physica A: Statistical Mechanics and its Applications, 2019, vol. 522, issue C, 215-231

Abstract: In this paper, a new framework for pricing the European currency option is developed in the case where the spot exchange rate follows a generalized mixed fractional Brownian motion with jumps (hereafter GJMFBM). In addition we consider a general case that the coefficients of the model are time-varying. To capture the behaviors of exchange rate, the combination of Poisson jumps and generalized mixed fractional Brownian motion is introduced. To derive the pricing formula for some options, we firstly derive a generalized mixed fractional Girsanov theorem and some results regarding the quasi-conditional expectation that we will need for the rest of the paper. Then analytic pricing formulas for European currency option and exchange option are obtained using the equivalent martingale measure. Finally, through some numerical experiments and discussion we show that the GJMFBM model is different with the other previous ones.

Keywords: European currency option; Generalized mixed fractional Brownian motion; Exchange option; Jump (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:522:y:2019:i:c:p:215-231

DOI: 10.1016/j.physa.2019.01.145

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