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An efficient and stable method for short maturity Asian options

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  • Rupak Chatterjee
  • Zhenyu Cui
  • Jiacheng Fan
  • Mingzhe Liu

Abstract

In this paper, we develop a Markov chain‐based approximation method to price arithmetic Asian options for short maturities under the case of geometric Brownian motion. It has the advantage of being a closed‐form approximation involving only matrices. It is an accurate, efficient, and stable method for the pricing and hedging of short maturity arithmetic Asian options for which previous methods in the literature have shown either slower convergence or instabilities in hedging parameters. We demonstrate that this method is as good as and sometimes better than existing approximation methods in the literature.

Suggested Citation

  • Rupak Chatterjee & Zhenyu Cui & Jiacheng Fan & Mingzhe Liu, 2018. "An efficient and stable method for short maturity Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(12), pages 1470-1486, December.
    • Handle: RePEc:wly:jfutmk:v:38:y:2018:i:12:p:1470-1486
    DOI: 10.1002/fut.21956
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    References listed on IDEAS

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    1. Vicky Henderson & Rafal Wojakowski, 2001. "On the Equivalence of Floating and Fixed-Strike Asian Options," OFRC Working Papers Series 2001mf08, Oxford Financial Research Centre.
    2. Tian, Yisong S., 2013. "Ironing out the kinks in executive compensation: Linking incentive pay to average stock prices," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 415-432.
    3. Brian J. Hall & Kevin J. Murphy, 2003. "The Trouble with Stock Options," Journal of Economic Perspectives, American Economic Association, vol. 17(3), pages 49-70, Summer.
    4. Zhenyu Cui & Runhuan Feng & Anne MacKay, 2017. "Variable Annuities with VIX-Linked Fee Structure under a Heston-Type Stochastic Volatility Model," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 458-483, July.
    5. Ning Cai & Yingda Song & Steven Kou, 2015. "A General Framework for Pricing Asian Options Under Markov Processes," Operations Research, INFORMS, vol. 63(3), pages 540-554, June.
    6. Johnson, Shane A. & Tian, Yisong S., 2000. "Indexed executive stock options," Journal of Financial Economics, Elsevier, vol. 57(1), pages 35-64, July.
    7. Peter Carr & Michael Schroder, 2001. "On the valuation of arithmetic-average Asian options: the Geman-Yor Laplace transform revisited," Papers math/0102080, arXiv.org.
    8. Johnson, Shane A. & Tian, Yisong S., 2000. "The value and incentive effects of nontraditional executive stock option plans," Journal of Financial Economics, Elsevier, vol. 57(1), pages 3-34, July.
    9. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2017. "Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 46-62.
    10. Dan Pirjol & Lingjiong Zhu, 2016. "Short Maturity Asian Options in Local Volatility Models," Papers 1609.07559, arXiv.org.
    11. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    12. 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.
    13. Dutt, Tanuj & Humphery-Jenner, Mark, 2013. "Stock return volatility, operating performance and stock returns: International evidence on drivers of the ‘low volatility’ anomaly," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 999-1017.
    14. Dan Pirjol & Lingjiong Zhu, 2017. "Short Maturity Asian Options for the CEV Model," Papers 1702.03382, arXiv.org.
    15. 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.
    16. Brian J. Hall & Kevin J. Murphy, 2003. "The Trouble with Stock Options," NBER Working Papers 9784, National Bureau of Economic Research, Inc.
    17. Cui, Zhenyu & Lee, Chihoon & Liu, Yanchu, 2018. "Single-transform formulas for pricing Asian options in a general approximation framework under Markov processes," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1134-1139.
    18. C. Brown & J. C. Handley & C.-T. Lin & K. J. Palmer, 2016. "Partial differential equations for Asian option prices," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 447-460, March.
    19. Stambaugh, Robert F. & Yu, Jianfeng & Yuan, Yu, 2012. "The short of it: Investor sentiment and anomalies," Journal of Financial Economics, Elsevier, vol. 104(2), pages 288-302.
    20. Chuang-Chang Chang & Chueh-Yung Tsao, 2011. "Efficient and accurate quadratic approximation methods for pricing Asian strike options," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 729-748.
    21. Andrew Lyasoff, 2016. "Another look at the integral of exponential Brownian motion and the pricing of Asian options," Finance and Stochastics, Springer, vol. 20(4), pages 1061-1096, October.
    22. Søren Asmussen & Jens Ledet Jensen & Leonardo Rojas-Nandayapa, 2016. "Exponential Family Techniques for the Lognormal Left Tail," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(3), pages 774-787, September.
    23. John E. Angus, 1999. "A note on pricing Asian derivatives with continuous geometric averaging," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 19(7), pages 845-858, October.
    24. P. E. Kloeden & Eckhard Platen, 1992. "Higher-order implicit strong numerical schemes for stochastic differential equations," Published Paper Series 1992-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    25. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    26. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2017. "A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps," European Journal of Operational Research, Elsevier, vol. 262(1), pages 381-400.
    27. Chueh‐Yung Tsao & Chuang‐Chang Chang & Chung‐Gee Lin, 2003. "Analytic approximation formulae for pricing forward‐starting Asian options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(5), pages 487-516, May.
    28. Kirkby, J. Lars & Nguyen, Duy & Cui, Zhenyu, 2017. "A unified approach to Bermudan and barrier options under stochastic volatility models with jumps," Journal of Economic Dynamics and Control, Elsevier, vol. 80(C), pages 75-100.
    29. Hoi Ying Wong & Ying Lok Cheung, 2004. "Geometric Asian options: valuation and calibration with stochastic volatility," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 301-314.
    30. Chih‐Hao Kao & Yuh‐Dauh Lyuu, 2003. "Pricing of moving‐average‐type options with applications," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 23(5), pages 415-440, May.
    31. Chia Chun Lo & Konstantinos Skindilias, 2014. "An Improved Markov Chain Approximation Methodology: Derivatives Pricing And Model Calibration," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-22.
    32. Carole Bernard & Zhenyu Cui & Steven Vanduffel, 2017. "Impact of Flexible Periodic Premiums on Variable Annuity Guarantees," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(1), pages 63-86, January.
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    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.
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    3. Ding, Kailin & Ning, Ning, 2021. "Markov chain approximation and measure change for time-inhomogeneous stochastic processes," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    4. Dan Pirjol & Lingjiong Zhu, 2024. "Short-maturity Asian options in local-stochastic volatility models," Papers 2409.08377, arXiv.org.

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