Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets
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 [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.
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- Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
- Bryan Routledge & Duane Seppi & Chester Spatt, .
"Equilibrium Forward Curves for Commodities,"
GSIA Working Papers
1997-50, Carnegie Mellon University, Tepper School of Business.
- Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor & Francis Journals, vol. 6(4), pages 337-347.
- Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, vol. 52(3), pages 923-73, July.
- Jaime Casassus & Pierre Collin-Dufresne, 2005. "Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates," Journal of Finance, American Finance Association, vol. 60(5), pages 2283-2331, October.
- Bessembinder, Hendrik, et al, 1995. " Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure," Journal of Finance, American Finance Association, vol. 50(1), pages 361-75, March.
- Cartea, Álvaro & Williams, Thomas, 2008.
"UK gas markets: The market price of risk and applications to multiple interruptible supply contracts,"
Elsevier, vol. 30(3), pages 829-846, May.
- Alvaro Cartea & Thomas Williams, 2006. "UK Gas Markets: the Market Price of Risk and Applications to Multiple Interruptible Supply Contracts," Birkbeck Working Papers in Economics and Finance 0608, Birkbeck, Department of Economics, Mathematics & Statistics.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Robert S. Pindyck, 2001. "The Dynamics of Commodity Spot and Futures Markets: A Primer," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 1-30.
- Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 474-491, October.
- Steen Koekebakker & Gudbrand Lien, 2004. "Volatility and Price Jumps in Agricultural Futures Prices—Evidence from Wheat Options," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(4), pages 1018-1031.
- 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.
- Regnier, Eva, 2007. "Oil and energy price volatility," Energy Economics, Elsevier, vol. 29(3), pages 405-427, May.
- Hélyette Geman & Andrea Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1225-1262, May.
- Helyette Geman & A. Roncoroni, 2006. "Understanding the Fine Structure of Electricity Prices," Post-Print halshs-00144198, HAL.
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