Commodity Asian Options: A Closed-Form Formula
University of Piemonte Orientale - Facoltà di Economia
University of Eastern Piedmont
ESSEC Business School
November 1, 2007
EFA 2008 Athens Meetings Paper
We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan (1999) [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61-73] allows us to derive a closed-form formula for the fair value of discretely-monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion.
Number of Pages in PDF File: 27
Keywords: Asian options, discrete monitoring, Laplace transform, Fourier transform, Commodity
JEL Classification: C63, G13working papers series
Date posted: March 6, 2008
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