IJPAM: Volume 76, No. 5 (2012)

PRICING OF AVERAGE STRIKE ASIAN
CALL OPTION USING NUMERICAL PDE METHODS

A. Kumar$^1$, A. Waikos$^2$, S.P. Chakrabarty$^3$
$^{1,2,3}$Department of Mathematics
IIT Guwahati
Guwahati, 781039, Assam, INDIA


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.

Received: December 8, 2011

AMS Subject Classification: 91G60

Key Words and Phrases: Asian option, Crank Nicolson implicit method, higher order compact, Monte Carlo simulation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 76
Issue: 5