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Asymptotic behavior of prices of path dependent options

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  • Yuji Hishida
  • Kenji Yasutomi
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    Abstract

    In this paper, we give a numerical method for pricing long maturity, path dependent options by using the Markov property for each underlying asset. This enables us to approximate a path dependent option by using some kinds of plain vanillas. We give some examples whose underlying assets behave as some popular Levy processes. Moreover, we give some payoffs and functions used to approximate them.

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    File URL: http://arxiv.org/pdf/0911.5579
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0911.5579.

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    Date of creation: Nov 2009
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    Handle: RePEc:arx:papers:0911.5579

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    Web page: http://arxiv.org/

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    1. Yuji Hishida & Kenji Yasutomi, 2005. "On the asymptotic behavior of the prices of Asian options," Asia-Pacific Financial Markets, Springer, Springer, vol. 12(4), pages 289-306, December.
    2. Hans-Peter Bermin, 2000. "Hedging lookback and partial lookback options using Malliavin calculus," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 7(2), pages 75-100.
    3. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, Springer, vol. 13(4), pages 471-500, September.
    4. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 3(4), pages 349-375.
    5. Grant Armstrong, 2001. "Valuation formulae for window barrier options," Applied Mathematical Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 8(4), pages 197-208.
    6. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    7. Hans-Peter Bermin, 2002. "A General Approach to Hedging Options: Applications to Barrier and Partial Barrier Options," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 12(3), pages 199-218.
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