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Pricing and Hedging of Asian Options: Quasi-Explicit Solutions via Malliavin Calculus

  • Zhaojun Yang
  • Christian-Oliver Ewald
  • Olaf Menkens

We use Malliavin calculus and the Clark-Ocone formula to derive the hedging strategy of an arithmetic Asian Call option in general terms. Furthermore we derive an expression for the density of the integral over time of a geometric Brownian motion, which allows us to express hedging strategy and price of the Asian option as an analytic, that is closed form, expression. Numerical computations which are based on this expression are provided.

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Paper provided by Centre for Research into Industry, Enterprise, Finance and the Firm in its series CRIEFF Discussion Papers with number 0910.

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Date of creation: Sep 2009
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Handle: RePEc:san:crieff:0910
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  1. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
  2. Hélyette Geman & Marc Yor, 1996. "Pricing And Hedging Double-Barrier Options: A Probabilistic Approach," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 365-378.
  3. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
  4. Jorge A. León & Reyla Navarro & David Nualart, 2003. "An Anticipating Calculus Approach to the Utility Maximization of an Insider," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 171-185.
  5. Peter Carr & Christian-Oliver Ewald & Yajun Xiao, 2008. "On the Qualitative Effect of Volatility and Duration on Prices of Asian Options," CRIEFF Discussion Papers 0803, Centre for Research into Industry, Enterprise, Finance and the Firm.
  6. Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
  7. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
  8. Simon, S. & Goovaerts, M. J. & Dhaene, J., 2000. "An easy computable upper bound for the price of an arithmetic Asian option," Insurance: Mathematics and Economics, Elsevier, vol. 26(2-3), pages 175-183, May.
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