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Pricing currency options in the mixed fractional Brownian motion

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  • Sun, Lin

Abstract

This paper deals with the problem of pricing European currency options in the mixed fractional Brownian environment. Both the pricing formula and the mixed fractional partial differential equation for European call currency options are obtained. Some Greeks and the estimator of volatility are also provided. Empirical studies and simulation results confirm the theoretical findings and show that the mixed fractional Brownian pricing model is a reasonable one.

Suggested Citation

  • Sun, Lin, 2013. "Pricing currency options in the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(16), pages 3441-3458.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:16:p:3441-3458
    DOI: 10.1016/j.physa.2013.03.055
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    5. Kim, Kyong-Hui & Kim, Nam-Ung & Ju, Dong-Chol & Ri, Ju-Hyang, 2020. "Efficient hedging currency options in fractional Brownian motion model with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
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    7. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 240-248.
    8. Ying Chang & Yiming Wang & Sumei Zhang, 2021. "Option Pricing under Double Heston Jump-Diffusion Model with Approximative Fractional Stochastic Volatility," Mathematics, MDPI, vol. 9(2), pages 1-10, January.
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    14. Alexander Kukush & Stanislav Lohvinenko & Yuliya Mishura & Kostiantyn Ralchenko, 2022. "Two approaches to consistent estimation of parameters of mixed fractional Brownian motion with trend," Statistical Inference for Stochastic Processes, Springer, vol. 25(1), pages 159-187, April.
    15. Yang, Zhaoqiang, 2020. "Default probability of American lookback option in a mixed jump-diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    16. Foad Shokrollahi & Davood Ahmadian & Luca Vincenzo Ballestra, 2021. "Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps," Papers 2105.06999, arXiv.org.
    17. Axel A. Araneda, 2019. "The fractional and mixed-fractional CEV model," Papers 1903.05747, arXiv.org, revised Jun 2019.
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    20. Chen, Wenting & Yan, Bowen & Lian, Guanghua & Zhang, Ying, 2016. "Numerically pricing American options under the generalized mixed fractional Brownian motion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 180-189.

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