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Pricing arithmetic Asian options under jump diffusion CIR processes

Author

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  • Park, Jong Jun
  • Jang, Hyun Jin
  • Jang, Jiwook

Abstract

We compute analytical formulae for pricing arithmetic Asian options under jump diffusion CIR processes. To derive the solution, we employ a characteristic function of the underlying asset price process and its integrated process that is not required to take the inversion Fourier or Laplace transform. We conduct numerical tests for validation of proposed formulae to confirm that they provide stable and accurate option prices with much faster computation time than the full Monte Carlo method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:finlet:v:34:y:2020:i:c:s1544612318305099
    DOI: 10.1016/j.frl.2019.08.017
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    References listed on IDEAS

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    1. 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.
    2. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    3. Moshe Arye Milevsky & Steven E. Posner, 1999. "Asian Options, The Sum Of Lognormals, And The Reciprocal Gamma Distribution," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar, chapter 7, pages 203-218, World Scientific Publishing Co. Pte. Ltd..
    4. Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
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    8. Jang, Jiwook, 2007. "Jump diffusion processes and their applications in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 41(1), pages 62-70, July.
    9. Daniel Dufresne, 2005. "Bessel Processes and Asian Options," Springer Books, in: Michèle Breton & Hatem Ben-Ameur (ed.), Numerical Methods in Finance, chapter 0, pages 35-57, Springer.
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    Cited by:

    1. Jang, Jiwook & Qu, Yan & Zhao, Hongbiao & Dassios, Angelos, 2023. "A Cox model for gradually disappearing events," LSE Research Online Documents on Economics 112754, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Jump diffusion CIR processes; Joint Fourier and Laplace transforms; Characteristic functions; Arithmetic Asian options;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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