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

Author

Listed:
  • 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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    1. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    2. Zhigang Tong, 2017. "Modelling VIX and VIX derivatives with reducible diffusions," International Journal of Bonds and Derivatives, Inderscience Enterprises Ltd, vol. 3(2), pages 153-175.
    3. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    4. Bu, Ruijun & Cheng, Jie & Hadri, Kaddour, 2016. "Reducible diffusions with time-varying transformations with application to short-term interest rates," Economic Modelling, Elsevier, vol. 52(PA), pages 266-277.
    5. Lingfei Li & Rafael Mendoza-Arriaga & Zhiyu Mo & Daniel Mitchell, 2016. "Modelling electricity prices: a time change approach," Quantitative Finance, Taylor & Francis Journals, vol. 16(7), pages 1089-1109, July.
    6. 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.
    7. Fusai, Gianluca & Marena, Marina & Roncoroni, Andrea, 2008. "Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2033-2045, October.
    8. Dongjae Lim & Lingfei Li & Vadim Linetsky, 2012. "Evaluating Callable and Putable Bonds: An Eigenfunction Expansion Approach," Papers 1206.5046, arXiv.org.
    9. Ruijun Bu & Ludovic Giet & Kaddour Hadri & Michel Lubrano, 2011. "Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 9(1), pages 198-236, Winter.
    10. Li, Jing & Li, Lingfei & Zhang, Gongqiu, 2017. "Pure jump models for pricing and hedging VIX derivatives," Journal of Economic Dynamics and Control, Elsevier, vol. 74(C), pages 28-55.
    11. Lim, Dongjae & Li, Lingfei & Linetsky, Vadim, 2012. "Evaluating callable and putable bonds: An eigenfunction expansion approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1888-1908.
    12. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
    13. Vadim Linetsky, 2004. "The Spectral Decomposition Of The Option Value," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 337-384.
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    Cited by:

    1. 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).
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    3. 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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