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Asymptotic behavior of prices of path dependent options

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  • Yuji Hishida
  • Kenji Yasutomi

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.

Suggested Citation

  • Yuji Hishida & Kenji Yasutomi, 2009. "Asymptotic behavior of prices of path dependent options," Papers 0911.5579, arXiv.org.
    • Handle: RePEc:arx:papers:0911.5579
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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. 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..
    3. 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.
    4. E. Benhamou, 2001. "Fast Fourier Transform for discrete Asian Options," Computing in Economics and Finance 2001 6, Society for Computational Economics.
    5. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375, October.
    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, July.
    7. 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.
    8. Vadim Linetsky, 2004. "Spectral Expansions for Asian (Average Price) Options," Operations Research, INFORMS, vol. 52(6), pages 856-867, December.
    9. Oleg Kudryavtsev & Sergei Levendorskiǐ, 2009. "Fast and accurate pricing of barrier options under Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 531-562, September.
    10. Grant Armstrong, 2001. "Valuation formulae for window barrier options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 8(4), pages 197-208.
    11. Yuji Hishida & Kenji Yasutomi, 2005. "On the asymptotic behavior of the prices of Asian options," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(4), pages 289-306, December.
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