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Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps

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  • Chung, Shing Fung
  • Wong, Hoi Ying

Abstract

Empirical evidence indicates that commodity prices are mean reverting and exhibit jumps. As some commodity option payoffs involve the arithmetic average of historical commodity prices, we derive an analytical solution to arithmetic Asian options under a mean reverting jump diffusion process. The analytical solution is implemented with the fast Fourier transform based on the joint characteristic function of the terminal asset price and the realized average value. We also examine the accuracy and computational efficiency of the proposed method through numerical studies.

Suggested Citation

  • Chung, Shing Fung & Wong, Hoi Ying, 2014. "Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 130-140.
    • Handle: RePEc:eee:jbfina:v:44:y:2014:i:c:p:130-140
    DOI: 10.1016/j.jbankfin.2014.04.011
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    References listed on IDEAS

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    9. Fuh, Cheng-Der & Luo, Sheng-Feng & Yen, Ju-Fang, 2013. "Pricing discrete path-dependent options under a double exponential jump–diffusion model," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 2702-2713.
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    Cited by:

    1. Song, Shiyu, 2024. "The valuation of arithmetic Asian options with mean reversion and jump clustering," The North American Journal of Economics and Finance, Elsevier, vol. 70(C).
    2. Zhang, Wei-Guo & Li, Zhe & Liu, Yong-Jun, 2018. "Analytical pricing of geometric Asian power options on an underlying driven by a mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 402-418.
    3. Park, Jong Jun & Jang, Hyun Jin & Jang, Jiwook, 2020. "Pricing arithmetic Asian options under jump diffusion CIR processes," Finance Research Letters, Elsevier, vol. 34(C).
    4. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de Opciones Call Asiáticas Promedio Aritmético bajo Movimiento Browniano Logístico," Working Papers 46, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.
    5. Wu, Bin & Chen, Pengzhan & Ye, Wuyi, 2024. "Variance swaps with mean reversion and multi-factor variance," European Journal of Operational Research, Elsevier, vol. 315(1), pages 191-212.
    6. Susana Alvarez Diez & Samuel Baixauli & Luis Eduardo Girón, 2019. "Valoración de opciones call asiáticas Promedio Aritmético usando Taylor Estocástico 1.5," Working Papers 44, Faculty of Economics and Management, Pontificia Universidad Javeriana Cali.
    7. Zhigang Tong & Allen Liu, 2018. "Analytical pricing of discrete arithmetic Asian options under generalized CIR process with time change," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(01), pages 1-21, March.
    8. Pun, Chi Seng & Chung, Shing Fung & Wong, Hoi Ying, 2015. "Variance swap with mean reversion, multifactor stochastic volatility and jumps," European Journal of Operational Research, Elsevier, vol. 245(2), pages 571-580.
    9. Ying Wang & Sai Tsang Boris Choy & Hoi Ying Wong, 2016. "Bayesian Option Pricing Framework with Stochastic Volatility for FX Data," Risks, MDPI, vol. 4(4), pages 1-12, December.
    10. Jiwook Jang & Jong Jun Park & Hyun Jin Jang, 2018. "Catastrophe Insurance Derivatives Pricing Using A Cox Process With Jump Diffusion Cir Intensity," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(07), pages 1-20, November.

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    More about this item

    Keywords

    Asian options; Fourier transform; Mean reversion; Jump diffusion;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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