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Commodity Asian Options: A Closed-Form Formula

27 Pages Posted: 6 Mar 2008  

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa; Cass Business School, City University London

Marina Marena

University of Eastern Piedmont

Andrea Roncoroni

ESSEC Business School

Date Written: November 1, 2007

Abstract

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.

Keywords: Asian options, discrete monitoring, Laplace transform, Fourier transform, Commodity

JEL Classification: C63, G13

Suggested Citation

Fusai, Gianluca and Marena, Marina and Roncoroni, Andrea, Commodity Asian Options: A Closed-Form Formula (November 1, 2007). EFA 2008 Athens Meetings Paper. Available at SSRN: https://ssrn.com/abstract=1100605 or http://dx.doi.org/10.2139/ssrn.1100605

Gianluca Fusai

Università del Piemonte Orientale Dipartimento di Studi per l'Economia e l'Impresa ( email )

Via Perrone, 18
Novara, 28100
Italy

HOME PAGE: http://https://upobook.uniupo.it/gianluca.fusai

Cass Business School, City University London ( email )

106 Bunhill Row
London, EC2Y 8HB
Great Britain

HOME PAGE: http:// www.cass.city.ac.uk/experts/G.Fusai

Marina Marena

University of Eastern Piedmont ( email )

Corso Borsalino 50
Department of Economics and Quantitative Methods
15100 Alessandria
Italy
+39 011 6706275 (Phone)

Andrea Roncoroni (Contact Author)

ESSEC Business School ( email )

Avenue Bernard Hirsch BP 50105
Cergy-Pontoise, 95021
France
+33 (0)1 34 43 32 39 (Phone)
+33 (0)1 34 43 30 01 (Fax)

HOME PAGE: http://www45.essec.edu/faculty/andrea-roncoroni

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