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Pricing of average strike Asian call option using numerical PDE methods

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  • Abhishek Kumar
  • Ashwin Waikos
  • Siddhartha P. Chakrabarty

Abstract

In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. The option prices for the same set of values of risk free rate and volatility was also computed using Monte Carlo simulation. The comparative results of the two numerical PDE methods shows close match with the Monte Carlo results, with the Higher Order Compact scheme exhibiting a better match. To the best of our knowledge, this is the first work to use the numerical PDE approach for pricing Asian call options with average strike.

Suggested Citation

  • Abhishek Kumar & Ashwin Waikos & Siddhartha P. Chakrabarty, 2011. "Pricing of average strike Asian call option using numerical PDE methods," Papers 1106.1999, arXiv.org.
    • Handle: RePEc:arx:papers:1106.1999
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    References listed on IDEAS

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    1. Higham,Desmond J., 2004. "An Introduction to Financial Option Valuation," Cambridge Books, Cambridge University Press, number 9780521547574, September.
    2. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893, September.
    3. Mark Broadie & Paul Glasserman, 1996. "Estimating Security Price Derivatives Using Simulation," Management Science, INFORMS, vol. 42(2), pages 269-285, February.
    4. Boyle, Phelim P., 1977. "Options: A Monte Carlo approach," Journal of Financial Economics, Elsevier, vol. 4(3), pages 323-338, May.
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