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The distribution of the average of log-normal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula

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  • Alghalith, Moawia

Abstract

We introduce a simple, exact and closed-form formula for pricing the arithmetic Asian options. The pricing formula is as simple as the classical Black-Scholes formula. In doing so, we show that the distribution of the continuous average of log-normal variables is log-normal.

Suggested Citation

  • Alghalith, Moawia, 2019. "The distribution of the average of log-normal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula," MPRA Paper 97324, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:97324
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    File URL: https://mpra.ub.uni-muenchen.de/101778/9/MPRA_paper_101778.pdf
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    References listed on IDEAS

    as
    1. Ales Cerny & Ioannis Kyriakou, 2010. "An improved convolution algorithm for discretely sampled Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 11(3), pages 381-389.
    2. Aprahamian, Hrayer & Maddah, Bacel, 2015. "Pricing Asian options via compound gamma and orthogonal polynomials," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 21-43.
    3. Sander Willems, 2019. "Asian option pricing with orthogonal polynomials," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 605-618, April.
    4. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    5. Bernard Lapeyre & Emmanuel Temam, 2001. "Competitive Monte Carlo methods for the pricing of Asian options," Post-Print hal-01667057, HAL.
    6. Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Arithmetic Asian option pricing; the arithmetic average of the price; average of log-normal; the Black-Scholes formula.;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • G0 - Financial Economics - - General

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