IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v264y2015icp21-43.html
   My bibliography  Save this article

Pricing Asian options via compound gamma and orthogonal polynomials

Author

Listed:
  • Aprahamian, Hrayer
  • Maddah, Bacel

Abstract

We develop two approximations (CG3 and CGn) for pricing arithmetic Asian options. Approximation CG3 utilizes a compound gamma distribution of the price average. It is calibrated by analytically matching the first three moments. Approximation CG3 outperforms many other existing approximations. Approximation CGn expands CG3 by utilizing the concept of orthogonal polynomials and matches n > 3 moments. It produces “near-exact” results, within 1 s, when volatility and maturity are not too high. Two useful insights of our work are (i) demonstrating that orthogonal polynomials can be used effectively to improve accuracy and (ii) showing that matching higher moments is beneficial.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:264:y:2015:i:c:p:21-43
    DOI: 10.1016/j.amc.2015.04.041
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315004993
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.04.041?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
    2. Jacques, Michel, 1996. "On the Hedging Portfolio of Asian Options," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 165-183, November.
    3. Marco Airoldi, 2005. "A moment expansion approach to option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 5(1), pages 89-104.
    4. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    5. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
    6. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 407-428, October.
    7. Giuseppe Campolieti & Roman Makarov, 2008. "Path integral pricing of Asian options on state-dependent volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 147-161.
    8. Allen Abrahamson, 2002. "All Moments of Discrete and Continuous Arithmetic Averages on Brownian Paths: A Closed Form," Finance 0205004, University Library of Munich, Germany.
    9. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(3), pages 377-389, September.
    10. 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..
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    12. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
    13. Corwin Joy & Phelim P. Boyle & Ken Seng Tan, 1996. "Quasi-Monte Carlo Methods in Numerical Finance," Management Science, INFORMS, vol. 42(6), pages 926-938, June.
    14. Eric Benhamou, 2002. "Smart Monte Carlo: various tricks using Malliavin calculus," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 329-336.
    15. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
    16. Satya Dubey, 1970. "Compound gamma, beta and F distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 16(1), pages 27-31, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sander Willems, 2018. "Asian Option Pricing with Orthogonal Polynomials," Papers 1802.01307, arXiv.org, revised Sep 2018.
    2. Alghalith, Moawia, 2019. "A New Price of the Arithmetic Asian Option: A Simple Formula," MPRA Paper 117047, University Library of Munich, Germany.
    3. Chih-Chen Hsu & Chung-Gee Lin & Tsung-Jung Kuo, 2020. "Pricing of Arithmetic Asian Options under Stochastic Volatility Dynamics: Overcoming the Risks of High-Frequency Trading," Mathematics, MDPI, vol. 8(12), pages 1-16, December.
    4. 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 105588, University Library of Munich, Germany.
    5. Geon Ho Choe & Minseok Kim, 2021. "Closed‐form lower bounds for the price of arithmetic average Asian options by multiple conditioning," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(12), pages 1916-1932, December.
    6. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chueh-Yung Tsao & Chao-Ching Liu, 2012. "Asian Options with Credit Risks: Pricing and Sensitivity Analysis," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 48(S3), pages 96-115, September.
    2. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
    3. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
    4. Jinke Zhou & Xiaolu Wang, 2008. "Accurate closed‐form approximation for pricing Asian and basket options," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 24(4), pages 343-358, July.
    5. Geon Ho Choe & Minseok Kim, 2021. "Closed‐form lower bounds for the price of arithmetic average Asian options by multiple conditioning," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(12), pages 1916-1932, December.
    6. Dai, Min & Li, Peifan & Zhang, Jin E., 2010. "A lattice algorithm for pricing moving average barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 542-554, March.
    7. Boyle, Phelim & Potapchik, Alexander, 2008. "Prices and sensitivities of Asian options: A survey," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 189-211, February.
    8. Sander Willems, 2018. "Asian Option Pricing with Orthogonal Polynomials," Papers 1802.01307, arXiv.org, revised Sep 2018.
    9. Jean-Yves Datey & Genevieve Gauthier & Jean-Guy Simonato, 2003. "The Performance of Analytical Approximations for the Computation of Asian Quanto-Basket Option Prices," Multinational Finance Journal, Multinational Finance Journal, vol. 7(1-2), pages 55-82, March-Jun.
    10. Keng‐Hsin Lo & Kehluh Wang & Ming‐Feng Hsu, 2008. "Pricing European Asian options with skewness and kurtosis in the underlying distribution," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(6), pages 598-616, June.
    11. Renyuan Shao & Brian Roe, 2003. "The design and pricing of fixed‐ and moving‐window contracts: An application of Asian‐Basket option pricing methods to the hog‐finishing sector," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(11), pages 1047-1073, November.
    12. Hatem Ben-Ameur & Michèle Breton & Pierre L'Ecuyer, 2002. "A Dynamic Programming Procedure for Pricing American-Style Asian Options," Management Science, INFORMS, vol. 48(5), pages 625-643, May.
    13. Tian-Shyr Dai & Yuh-Dauh Lyuu, 2002. "Efficient, exact algorithms for asian options with multiresolution lattices," Review of Derivatives Research, Springer, vol. 5(2), pages 181-203, May.
    14. Ewald, Christian-Oliver & Menkens, Olaf & Hung Marten Ting, Sai, 2013. "Asian and Australian options: A common perspective," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 1001-1018.
    15. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    16. Chiu, Chun-Yuan & Dai, Tian-Shyr & Lyuu, Yuh-Dauh, 2015. "Pricing Asian option by the FFT with higher-order error convergence rate under Lévy processes," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 418-437.
    17. Asbjørn T. Hansen & Peter Løchte Jørgensen, 2000. "Analytical Valuation of American-Style Asian Options," Management Science, INFORMS, vol. 46(8), pages 1116-1136, August.
    18. 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..
    19. Benhamou, Eric & Duguet, Alexandre, 2003. "Small dimension PDE for discrete Asian options," Journal of Economic Dynamics and Control, Elsevier, vol. 27(11), pages 2095-2114.
    20. He, Ting, 2023. "An imprecise pricing model for Asian options based on Nonparametric predictive inference," Pacific-Basin Finance Journal, Elsevier, vol. 77(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:264:y:2015:i:c:p:21-43. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.