IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1407.5091.html
   My bibliography  Save this paper

An exact and explicit formula for pricing Asian options with regime switching

Author

Listed:
  • Leunglung Chan
  • Song-Ping Zhu

Abstract

This paper studies the pricing of European-style Asian options when the price dynamics of the underlying risky asset are assumed to follow a Markov- modulated geometric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on unobservable states of the economy described by a continuous-time hidden Markov process. We derive the exact, explicit and closed-form solutions for European-style Asian options in a two-state regime switching model.

Suggested Citation

  • Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing Asian options with regime switching," Papers 1407.5091, arXiv.org.
  • Handle: RePEc:arx:papers:1407.5091
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1407.5091
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    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. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    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. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    11. Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.
    12. Peter Ritchken & L. Sankarasubramanian & Anand M. Vijh, 1993. "The Valuation of Path Dependent Contracts on the Average," Management Science, INFORMS, vol. 39(10), pages 1202-1213, October.
    13. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    14. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    15. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    16. 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.
    17. Robert J. Elliott & John van der Hoek, 1997. "An application of hidden Markov models to asset allocation problems (*)," Finance and Stochastics, Springer, vol. 1(3), pages 229-238.
    18. Robert J. Elliott & William C. Hunter & Barbara M. Jamieson, 2001. "Financial Signal Processing: A Self Calibrating Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 567-584.
    19. Fei Yuen & Hailiang Yang, 2010. "Pricing Asian Options and Equity-Indexed Annuities with Regime Switching by the Trinomial Tree Method," North American Actuarial Journal, Taylor & Francis Journals, vol. 14(2), pages 256-272.
    20. 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.
    21. Yuen, Fei Lung & Yang, Hailiang, 2009. "Option Pricing in a Jump-Diffusion Model with Regime Switching," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 515-539, November.
    22. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    23. Elliott, R. J. & Malcolm, W. P. & Tsoi, Allanus H., 2003. "Robust parameter estimation for asset price models with Markov modulated volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1391-1409, June.
    24. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
    25. Eberlein, Ernst & Papapantoleon, Antonis, 2005. "Equivalence of floating and fixed strike Asian and lookback options," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 31-40, January.
    Full references (including those not matched with items on IDEAS)

    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. Leunglung Chan & Song-Ping Zhu, 2021. "An Analytic Approach for Pricing American Options with Regime Switching," JRFM, MDPI, vol. 14(5), pages 1-20, April.
    2. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    3. Sin-Yu Ho & N.M. Odhiambo, 2018. "Analysing the macroeconomic drivers of stock market development in the Philippines," Cogent Economics & Finance, Taylor & Francis Journals, vol. 6(1), pages 1451265-145, January.
    4. 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.
    5. Sajid, M. & Hayat, T., 2008. "The application of homotopy analysis method to thin film flows of a third order fluid," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 506-515.
    6. Claudia García-García & Catalina B. García-García & Román Salmerón, 2021. "Confronting collinearity in environmental regression models: evidence from world data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(3), pages 895-926, September.
    7. Cambier, Adrien & Chardy, Matthieu & Figueiredo, Rosa & Ouorou, Adam & Poss, Michael, 2022. "Optimizing subscriber migrations for a telecommunication operator in uncertain context," European Journal of Operational Research, Elsevier, vol. 298(1), pages 308-321.
    8. Libura, Marek, 2007. "On the adjustment problem for linear programs," European Journal of Operational Research, Elsevier, vol. 183(1), pages 125-134, November.
    9. Christophe Loussouarn & Carine Franc & Yann Videau & Julien Mousquès, 2021. "Can General Practitioners Be More Productive? The Impact of Teamwork and Cooperation with Nurses on GP Activities," Health Economics, John Wiley & Sons, Ltd., vol. 30(3), pages 680-698, March.
    10. Tschakert, Petra, 2016. "Shifting Discourses of Vilification and the Taming of Unruly Mining Landscapes in Ghana," World Development, Elsevier, vol. 86(C), pages 123-132.
    11. María-Consuelo Casabán & Rafael Company & Lucas Jódar, 2020. "Non-Gaussian Quadrature Integral Transform Solution of Parabolic Models with a Finite Degree of Randomness," Mathematics, MDPI, vol. 8(7), pages 1-16, July.
    12. Isabelle Boutron & Peter John & David J. Torgerson, 2010. "Reporting Methodological Items in Randomized Experiments in Political Science," The ANNALS of the American Academy of Political and Social Science, , vol. 628(1), pages 112-131, March.
    13. Ben Slimane, Faten & Padilla Angulo, Laura, 2019. "Strategic change and corporate governance: Evidence from the stock exchange industry," Journal of Business Research, Elsevier, vol. 103(C), pages 206-218.
    14. Bossert, Walter & Derks, Jean & Peters, Hans, 2005. "Efficiency in uncertain cooperative games," Mathematical Social Sciences, Elsevier, vol. 50(1), pages 12-23, July.
    15. Weijun Xie & Yanfeng Ouyang & Sze Chun Wong, 2016. "Reliable Location-Routing Design Under Probabilistic Facility Disruptions," Transportation Science, INFORMS, vol. 50(3), pages 1128-1138, August.
    16. Natalia Nikolaevna Natocheeva* & Yuri Alexandrovich Rovensky & Yuri Yuryevich Rusanov & Tatiana Viktorovna Belyanchikova & Anna Anatolevna Staurskaya, 2018. "Optimizing Variability of Approaches to Regulatory Financing of Higher Education Services," The Journal of Social Sciences Research, Academic Research Publishing Group, pages 221-227:3.
    17. Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing lookback options with regime switching," Papers 1407.4864, arXiv.org.
    18. Philip Arestis & Howard Stein, 2005. "An Institutional Perspective to Finance and Development as an Alternative to Financial Liberalisation," International Review of Applied Economics, Taylor & Francis Journals, vol. 19(4), pages 381-398.
    19. Sahar Validi & Arijit Bhattacharya & P. J. Byrne, 2020. "Sustainable distribution system design: a two-phase DoE-guided meta-heuristic solution approach for a three-echelon bi-objective AHP-integrated location-routing model," Annals of Operations Research, Springer, vol. 290(1), pages 191-222, July.
    20. Cabada, Alberto & Fernández-Gómez, Carlos, 2015. "Constant sign solutions of two-point fourth order problems," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 122-133.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1407.5091. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.