IDEAS home Printed from https://ideas.repec.org/a/wly/jfutmk/v40y2020i6p974-988.html
   My bibliography  Save this article

Repeated Richardson extrapolation and static hedging of barrier options under the CEV model

Author

Listed:
  • Jia‐Hau Guo
  • Lung‐Fu Chang

Abstract

This paper proposes an accelerated static replication approach for continuous European‐style barrier options by employing the repeated Richardson extrapolation technique with the Romberg sequence. This approach is developed under the constant elasticity of variance (CEV) model of Cox (1975) and Cox and Ross (1976) using the framework offered by Derman, Ergener, and Kani (1995; DEK) and its modified method of Chung et al. (2010, 2013a, 2013b) and Tsai (2014). The numerical results indicate that our method could significantly reduce replication errors for European knock‐out call options and may be superior to the imposition of the theta‐matching condition on the DEK method.

Suggested Citation

  • Jia‐Hau Guo & Lung‐Fu Chang, 2020. "Repeated Richardson extrapolation and static hedging of barrier options under the CEV model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 974-988, June.
    • Handle: RePEc:wly:jfutmk:v:40:y:2020:i:6:p:974-988
    DOI: 10.1002/fut.22100
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/fut.22100
    Download Restriction: no
    File URL: https://libkey.io/10.1002/fut.22100?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. Ballestra, Luca Vincenzo & Cecere, Liliana, 2015. "Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley," Finance Research Letters, Elsevier, vol. 14(C), pages 45-55.
    2. San–Lin Chung & Mark B. Shackleton, 2007. "Generalised Geske‐‐Johnson Interpolation of Option Prices," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 34(5‐6), pages 976-1001, June.
    3. Emanuel, David C. & MacBeth, James D., 1982. "Further Results on the Constant Elasticity of Variance Call Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(4), pages 533-554, November.
    4. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
    5. Steven L. Heston & Mark Loewenstein & Gregory A. Willard, 2007. "Options and Bubbles," The Review of Financial Studies, Society for Financial Studies, vol. 20(2), pages 359-390.
    6. 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..
    7. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2015. "Pricing and static hedging of American-style knock-in options on defaultable stocks," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 343-360.
    8. San–Lin Chung & Mark B. Shackleton, 2007. "Generalised Geske‐‐Johnson Interpolation of Option Prices," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 34(5‐6), pages 976-1001, June.
    9. Nunes, João Pedro Vidal, 2009. "Pricing American Options under the Constant Elasticity of Variance Model and Subject to Bankruptcy," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 44(5), pages 1231-1263, October.
    10. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    11. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    12. Manuela Larguinho & José Carlos Dias & Carlos A. Braumann, 2013. "On the computation of option prices and Greeks under the CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 907-917, May.
    13. Chuang‐Chang Chang & San‐Lin Chung & Richard C. Stapleton, 2007. "Richardson extrapolation techniques for the pricing of American‐style options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(8), pages 791-817, August.
    14. San‐Lin Chung & Pai‐Ta Shih & Wei‐Che Tsai, 2010. "A modified static hedging method for continuous barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 30(12), pages 1150-1166, December.
    15. repec:bla:jfinan:v:53:y:1998:i:3:p:1165-1190 is not listed on IDEAS
    16. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    17. repec:bla:jfinan:v:44:y:1989:i:1:p:211-19 is not listed on IDEAS
    18. Peter Carr & Vadim Linetsky, 2006. "A jump to default extended CEV model: an application of Bessel processes," Finance and Stochastics, Springer, vol. 10(3), pages 303-330, September.
    19. Omberg, Edward, 1987. "A Note on the Convergence of Binomial-Pricing and Compound-Option," Journal of Finance, American Finance Association, vol. 42(2), pages 463-469, June.
    20. Bunch, David S & Johnson, Herb, 1992. "A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance, American Finance Association, vol. 47(2), pages 809-816, June.
    21. Benton, Denise & Krishnamoorthy, K., 2003. "Computing discrete mixtures of continuous distributions: noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 249-267, June.
    22. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    23. 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.
    24. Boyle, Phelim P. & Tian, Yisong “Sam”, 1999. "Pricing Lookback and Barrier Options under the CEV Process," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 241-264, June.
    25. Broadie, Mark & Detemple, Jerome, 1996. "American Option Valuation: New Bounds, Approximations, and a Comparison of Existing Methods," The Review of Financial Studies, Society for Financial Studies, vol. 9(4), pages 1211-1250.
    26. Tsai, Wei-Che, 2014. "Improved method for static replication under the CEV model," Finance Research Letters, Elsevier, vol. 11(3), pages 194-202.
    27. Dirk Veestraeten, 2017. "On the multiplicity of option prices under CEV with positive elasticity of variance," Review of Derivatives Research, Springer, vol. 20(1), pages 1-13, April.
    28. Dmitry Davydov & Vadim Linetsky, 2001. "Pricing and Hedging Path-Dependent Options Under the CEV Process," Management Science, INFORMS, vol. 47(7), pages 949-965, July.
    29. Aricson Cruz & José Carlos Dias, 2017. "The Binomial CEV Model and the Greeks," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 37(1), pages 90-104, January.
    30. Lung‐Fu Chang & Jia‐Hau Guo & Mao‐Wei Hung, 2016. "A Generalization of the Recursive Integration Method for the Analytic Valuation of American Options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(9), pages 887-901, September.
    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. Xiwei Yu & Qing Hu & Yudong Sun, 2023. "A Cubic B-Spline Collocation Method for Barrier Options under the CEV Model," Mathematics, MDPI, vol. 11(18), pages 1-18, September.

    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. Aricson Cruz & José Carlos Dias, 2020. "Valuing American-style options under the CEV model: an integral representation based method," Review of Derivatives Research, Springer, vol. 23(1), pages 63-83, April.
    2. José Carlos Dias & João Pedro Vidal Nunes & Aricson Cruz, 2020. "A note on options and bubbles under the CEV model: implications for pricing and hedging," Review of Derivatives Research, Springer, vol. 23(3), pages 249-272, October.
    3. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    4. Jos� Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, vol. 15(12), pages 1995-2010, December.
    5. Dias, José Carlos & Nunes, João Pedro Vidal & da Silva, Fernando Correia, 2024. "Finite maturity caps and floors on continuous flows under the constant elasticity of variance process," European Journal of Operational Research, Elsevier, vol. 316(1), pages 361-385.
    6. Carlos Miguel Glória & José Carlos Dias & Aricson Cruz, 2024. "Pricing levered warrants under the CEV diffusion model," Review of Derivatives Research, Springer, vol. 27(1), pages 55-84, April.
    7. Vidal Nunes, João Pedro & Ruas, João Pedro & Dias, José Carlos, 2015. "Pricing and static hedging of American-style knock-in options on defaultable stocks," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 343-360.
    8. Dias, José Carlos & Vidal Nunes, João Pedro, 2018. "Universal recurrence algorithm for computing Nuttall, generalized Marcum and incomplete Toronto functions and moments of a noncentral χ2 random variable," European Journal of Operational Research, Elsevier, vol. 265(2), pages 559-570.
    9. Deng Guohe & Xue Guangming, 2016. "Valuation of American Continuous-Installment Options Under the Constant Elasticity of Variance Model," Journal of Systems Science and Information, De Gruyter, vol. 4(2), pages 149-168, April.
    10. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007, January-A.
    11. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 25, July-Dece.
    12. Axel A. Araneda & Marcelo J. Villena, 2018. "Computing the CEV option pricing formula using the semiclassical approximation of path integral," Papers 1803.10376, arXiv.org.
    13. Tsai, Wei-Che, 2014. "Improved method for static replication under the CEV model," Finance Research Letters, Elsevier, vol. 11(3), pages 194-202.
    14. Igor V. Kravchenko & Vladislav V. Kravchenko & Sergii M. Torba & Jos'e Carlos Dias, 2017. "Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representation," Papers 1712.08247, arXiv.org.
    15. Igor V. Kravchenko & Vladislav V. Kravchenko & Sergii M. Torba & José Carlos Dias, 2019. "Pricing Double Barrier Options On Homogeneous Diffusions: A Neumann Series Of Bessel Functions Representation," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(06), pages 1-24, September.
    16. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    17. B. Gao J. Huang, "undated". "The Valuation of American Barrier Options Using the Decomposition Technique," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-002, New York University, Leonard N. Stern School of Business-.
    18. San–Lin Chung & Mark B. Shackleton, 2007. "Generalised Geske‐‐Johnson Interpolation of Option Prices," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 34(5‐6), pages 976-1001, June.
    19. Lung-Fu Chang & Mao-Wei Hung, 2006. "Valuation of vulnerable American options with correlated credit risk," Review of Derivatives Research, Springer, vol. 9(2), pages 137-165, September.
    20. Ballestra, Luca Vincenzo & Cecere, Liliana, 2015. "Pricing American options under the constant elasticity of variance model: An extension of the method by Barone-Adesi and Whaley," Finance Research Letters, Elsevier, vol. 14(C), pages 45-55.

    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:40:y:2020:i:6:p:974-988. 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.