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A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options

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  • Sam Howison
  • Mario Steinberg

Abstract

This paper discusses the 'continuity correction' that should be applied to relate the prices of discretely sampled barrier options and their continuously-sampled equivalents. Using a matched asymptotic expansions approach it is shown that the correction of Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) can be applied in a very wide variety of cases. The correction to higher order is calculated in terms of the expansion parameter (the scaled time between resets) and it is shown how to apply the correction in jump-diffusion and local volatility models.

Suggested Citation

  • Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
  • Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:63-89
    DOI: 10.1080/13504860600858402
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    References listed on IDEAS

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    1. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
    2. Sam Howison, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 91-104.
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    Cited by:

    1. Xiao, Shuang & Ma, Shihua, 2016. "Pricing discrete double barrier options under Lévy processes: An extension of the method by Milev and Tagliani," Finance Research Letters, Elsevier, vol. 19(C), pages 67-74.
    2. Liming Feng & Vadim Linetsky, 2008. "Pricing Discretely Monitored Barrier Options And Defaultable Bonds In Lévy Process Models: A Fast Hilbert Transform Approach," Mathematical Finance, Wiley Blackwell, vol. 18(3), pages 337-384.
    3. Lingfei Li & Vadim Linetsky, 2015. "Discretely monitored first passage problems and barrier options: an eigenfunction expansion approach," Finance and Stochastics, Springer, vol. 19(4), pages 941-977, October.
    4. Sam Howison & Mario Steinberg, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 63-89.
    5. Sam Howison, 2007. "A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(1), pages 91-104.
    6. repec:eee:dyncon:v:83:y:2017:i:c:p:198-214 is not listed on IDEAS
    7. Lian, Guanghua & Zhu, Song-Ping & Elliott, Robert J. & Cui, Zhenyu, 2017. "Semi-analytical valuation for discrete barrier options under time-dependent Lévy processes," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 167-183.
    8. Michael B. Giles & Francisco Bernal, 2017. "Multilevel estimation of expected exit times and other functionals of stopped diffusions," Papers 1710.07492, arXiv.org.
    9. Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, François, 2008. "Pricing derivatives with barriers in a stochastic interest rate environment," Journal of Economic Dynamics and Control, Elsevier, vol. 32(9), pages 2903-2938, September.
    10. repec:eee:apmaco:v:251:y:2015:i:c:p:363-377 is not listed on IDEAS

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