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Random walk duality and the valuation of discrete lookback options

Author

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  • Farid Aitsahlia
  • Tzeung Le Lai

Abstract

Use is made of the duality property of random walks to develop a numerical method for the valuation of discrete-time lookback options. This method leads to a recursive numerical integration procedure which is fast, accurate and easy to implement.

Suggested Citation

  • Farid Aitsahlia & Tzeung Le Lai, 1998. "Random walk duality and the valuation of discrete lookback options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(3-4), pages 227-240.
    • Handle: RePEc:taf:apmtfi:v:5:y:1998:i:3-4:p:227-240
    DOI: 10.1080/135048698334655
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    References listed on IDEAS

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    1. Conze, Antoine & Viswanathan, 1991. "Path Dependent Options: The Case of Lookback Options," Journal of Finance, American Finance Association, vol. 46(5), pages 1893-1907, December.
    2. Goldman, M Barry & Sosin, Howard B & Shepp, Lawrence A, 1979. "On Contingent Claims That Insure Ex-post Optimal Stock Market Timing," Journal of Finance, American Finance Association, vol. 34(2), pages 401-413, May.
    3. R. C. Heynen & H. M. Kat, 1995. "Lookback options with discrete and partial monitoring of the underlying price," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(4), pages 273-284.
    4. Paul Glasserman & S.G. Kou & Mark Broadie, 1999. "Connecting discrete and continuous path-dependent options," Finance and Stochastics, Springer, vol. 3(1), pages 55-82.
    5. Cheuk, Terry H. F. & Vorst, Ton C. F., 1997. "Currency lookback options and observation frequency: A binomial approach," Journal of International Money and Finance, Elsevier, vol. 16(2), pages 173-187, April.
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    Citations

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    Cited by:

    1. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Lookback Option Pricing under Markov Models," Papers 2112.00439, arXiv.org.
    2. Liming Feng & Vadim Linetsky, 2009. "Computing exponential moments of the discrete maximum of a Lévy process and lookback options," Finance and Stochastics, Springer, vol. 13(4), pages 501-529, September.
    3. Houllier, Melanie & Murphy, David, 2017. "Borderline: judging the adequacy of return distribution estimation techniques in initial margin models," Bank of England working papers 673, Bank of England.
    4. Kim, Geonwoo & Jeon, Junkee, 2018. "Closed-form solutions for valuing partial lookback options with random initiation," Finance Research Letters, Elsevier, vol. 24(C), pages 321-327.
    5. Fusai, Gianluca & Recchioni, Maria Cristina, 2007. "Analysis of quadrature methods for pricing discrete barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 826-860, March.

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