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Analytical pricing of discrete arithmetic Asian options under generalized CIR process with time change

Author

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  • Zhigang Tong

    (Department of Mathematics and Statistics, University of Ottawa, 585 King Edward, Ottawa, Ontario, K1N 6N5, Canada)

  • Allen Liu

    (#x2020;Model Validation, Enterprise Risk and Portfolio Management, Bank of Montreal, 27th Floor, First Canadian Place, Toronto, Ontario, M5X 1A3, Canada)

Abstract

Starting from CIR process, we build a new model for pricing discrete arithmetic Asian options with nonlinear transformation and stochastic time change. The new model introduces the nonlinearity in both drift and diffusion components of the underlying process and allows for flexible jump processes. We are able to derive the recursive formula for the moment generating function of average price by employing the eigenfunction expansion technique. The Asian option prices can then be implemented through a Fourier transform. We also investigate the sensitivities of option prices with respect to the parameters of the new model.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijfexx:v:05:y:2018:i:01:n:s2424786318500020
    DOI: 10.1142/S2424786318500020
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    References listed on IDEAS

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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. Tong, Zhigang & Liu, Allen, 2022. "Pricing variance swaps under subordinated Jacobi stochastic volatility models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    3. Tong, Zhigang & Liu, Allen, 2021. "A censored Ornstein–Uhlenbeck process for rainfall modeling and derivatives pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    4. Kevin Z. Tong & Allen Liu, 2019. "Option pricing in a subdiffusive constant elasticity of variance (CEV) model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-21, June.

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