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Asymptotic behavior of prices of path dependent options

  • Yuji Hishida
  • Kenji Yasutomi
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    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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    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
    Contact details of provider: Web page: http://arxiv.org/

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