IDEAS home Printed from https://ideas.repec.org/a/wly/jfutmk/v41y2021i12p1916-1932.html
   My bibliography  Save this article

Closed‐form lower bounds for the price of arithmetic average Asian options by multiple conditioning

Author

Listed:
  • Geon Ho Choe
  • Minseok Kim

Abstract

We present closed‐form lower bounds for the price of arithmetic average Asian options under geometric Brownian motion. Lower bounds are found by conditioning on multiple normal variables, each of which is a weighted sum of Brownian motions. Numerical results show that our lower bounds are close to Monte Carlo prices and improve single conditioning methods especially for high volatility and long maturity.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:jfutmk:v:41:y:2021:i:12:p:1916-1932
    DOI: 10.1002/fut.22265
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/fut.22265
    Download Restriction: no
    File URL: https://libkey.io/10.1002/fut.22265?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
    ---><---

    References listed on IDEAS

    as
    1. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
    2. Daniel Dufresne, 2000. "Laguerre Series for Asian and Other Options," Mathematical Finance, Wiley Blackwell, vol. 10(4), pages 407-428, October.
    3. Pingping Zeng & Yue Kuen Kwok, 2016. "Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1375-1391, September.
    4. Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(2), pages 449-473, June.
    5. Kwangil Bae, 2019. "Valuation and applications of compound basket options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(6), pages 704-720, June.
    6. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    7. 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.
    8. Kyungsub Lee, 2014. "Recursive Formula for Arithmetic Asian Option Prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(3), pages 220-234, March.
    9. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
    10. Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
    11. Kemal Dinçer Dingeç & Halis Sak & Wolfgang Hörmann, 2015. "Variance Reduction for Asian Options under a General Model Framework," Review of Finance, European Finance Association, vol. 19(2), pages 907-949.
    12. Jacques, Michel, 1996. "On the Hedging Portfolio of Asian Options," ASTIN Bulletin, Cambridge University Press, vol. 26(2), pages 165-183, November.
    13. Dingeç, Kemal Dinçer & Hörmann, Wolfgang, 2013. "Control variates and conditional Monte Carlo for basket and Asian options," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 421-434.
    14. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    15. 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.
    16. 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..
    17. Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
    18. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
    19. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    20. Gianluca Fusai & Ioannis Kyriakou, 2016. "General Optimized Lower and Upper Bounds for Discrete and Continuous Arithmetic Asian Options," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 531-559, May.
    21. 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.
    22. 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.
    23. 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.
    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. Kailin Ding & Zhenyu Cui & Xiaoguang Yang, 2023. "Pricing arithmetic Asian and Amerasian options: A diffusion operator integral expansion approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 43(2), pages 217-241, February.

    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. 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.
    2. Jianqiang Sun & Langnan Chen & Shiyin Li, 2013. "A Quasi‐Analytical Pricing Model for Arithmetic Asian Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 33(12), pages 1143-1166, December.
    3. 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.
    4. Sander Willems, 2018. "Asian Option Pricing with Orthogonal Polynomials," Papers 1802.01307, arXiv.org, revised Sep 2018.
    5. Manuel Moreno & Javier F. Navas, 2008. "Australian Options," Australian Journal of Management, Australian School of Business, vol. 33(1), pages 69-93, June.
    6. Manuel Moreno & Javier F. Navas, 2003. "Australian Asian options," Economics Working Papers 680, Department of Economics and Business, Universitat Pompeu Fabra.
    7. 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.
    8. 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.
    9. Lemmens, D. & Liang, L.Z.J. & Tempere, J. & De Schepper, A., 2010. "Pricing bounds for discrete arithmetic Asian options under Lévy models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(22), pages 5193-5207.
    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. 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.
    12. 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.
    13. Ruggero Caldana & Gianluca Fusai & Alessandro Gnoatto & Martino Grasselli, 2016. "General closed-form basket option pricing bounds," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 535-554, April.
    14. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    15. Xu, Guoping & Zheng, Harry, 2009. "Approximate basket options valuation for a jump-diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 188-194, October.
    16. Dan Pirjol & Lingjiong Zhu, 2017. "Asymptotics for the Discrete-Time Average of the Geometric Brownian Motion and Asian Options," Papers 1706.09659, arXiv.org.
    17. H. Albrecher & P. A. Mayer & W. Schoutens, 2008. "General Lower Bounds for Arithmetic Asian Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 123-149.
    18. Pingping Zeng & Yue Kuen Kwok, 2016. "Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1375-1391, September.
    19. Jaehyuk Choi, 2018. "Sum of all Black–Scholes–Merton models: An efficient pricing method for spread, basket, and Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(6), pages 627-644, June.
    20. Hansjörg Albrecher & Philipp Mayer, 2010. "Semi-Static Hedging Strategies For Exotic Options," World Scientific Book Chapters, in: Rüdiger Kiesel & Matthias Scherer & Rudi Zagst (ed.), Alternative Investments And Strategies, chapter 14, pages 345-373, World Scientific Publishing Co. Pte. Ltd..

    More about this item

    Statistics

    Access and download statistics

    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:wly:jfutmk:v:41:y:2021:i:12:p:1916-1932. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.interscience.wiley.com/jpages/0270-7314/ .

    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.