Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Banking & Finance.
Volume (Year): 32 (2008)
Issue (Month): 10 (October)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jbf
C63 G13 Asian options Discrete monitoring Laplace transform Fourier transform Commodity markets Energy markets;
Find related papers by JEL classification:
- C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Angelos Dassios & Jayalaxshmi Nagaradjasarma, 2006. "The square-root process and Asian options," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 6(4), pages 337-347.
- 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, Birkbeck, Department of Economics, Mathematics & Statistics
0608, Birkbeck, Department of Economics, Mathematics & Statistics.
- Cartea, Ãlvaro & Williams, Thomas, 2008. "UK gas markets: The market price of risk and applications to multiple interruptible supply contracts," Energy Economics, Elsevier, Elsevier, vol. 30(3), pages 829-846, May.
- Bessembinder, Hendrik, et al, 1995. " Mean Reversion in Equilibrium Asset Prices: Evidence from the Futures Term Structure," Journal of Finance, American Finance Association, American Finance Association, vol. 50(1), pages 361-75, March.
- Bryan R. Routledge & Duane J. Seppi & Chester S. Spatt, 2000.
"Equilibrium Forward Curves for Commodities,"
Journal of Finance, American Finance Association,
American Finance Association, vol. 55(3), pages 1297-1338, 06.
- Bryan Routledge & Duane Seppi & Chester Spatt, . "Equilibrium Forward Curves for Commodities," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 1997-49, Carnegie Mellon University, Tepper School of Business.
- Bryan Routledge & Duane Seppi & Chester Spatt, . "Equilibrium Forward Curves for Commodities," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 1997-50, Carnegie Mellon University, Tepper School of Business.
- Schwartz, Eduardo S, 1997. " The Stochastic Behavior of Commodity Prices: Implications for Valuation and Hedging," Journal of Finance, American Finance Association, American Finance Association, vol. 52(3), pages 923-73, July.
- Hï¿½lyette 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.
- Geman, HÃ©lyette & Roncoroni, AndrÃ©a, 2006. "Understanding the Fine Structure of Electricity Prices," Economics Papers from University Paris Dauphine 123456789/1433, Paris Dauphine University.
- Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, Cambridge University Press, vol. 26(03), pages 377-389, September.
- Robert S. Pindyck, 2001. "The Dynamics of Commodity Spot and Futures Markets: A Primer," The Energy Journal, International Association for Energy Economics, International Association for Energy Economics, vol. 0(Number 3), pages 1-30.
- Steen Koekebakker & Gudbrand Lien, 2004. "Volatility and Price Jumps in Agricultural Futures Pricesâ€”Evidence from Wheat Options," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, Agricultural and Applied Economics Association, vol. 86(4), pages 1018-1031.
- Levy, Edmond, 1992. "Pricing European average rate currency options," Journal of International Money and Finance, Elsevier, Elsevier, vol. 11(5), pages 474-491, October.
- HÃ©lyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 3(4), pages 349-375.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
- Regnier, Eva, 2007. "Oil and energy price volatility," Energy Economics, Elsevier, Elsevier, vol. 29(3), pages 405-427, May.
- Jaime Casassus & Pierre Collin-Dufresne, 2005. "Stochastic Convenience Yield Implied from Commodity Futures and Interest Rates," Journal of Finance, American Finance Association, American Finance Association, vol. 60(5), pages 2283-2331, October.
- Ãlvaro Cartea & Carlos GonzÃ¡lez-Pedraz, 2010.
"How much should we pay for interconnecting electricity markets? A real options approach,"
Business Economics Working Papers, Universidad Carlos III, Departamento de EconomÃa de la Empresa
wb103206, Universidad Carlos III, Departamento de EconomÃa de la Empresa.
- Cartea, Ãlvaro & GonzÃ¡lez-Pedraz, Carlos, 2012. "How much should we pay for interconnecting electricity markets? A real options approach," Energy Economics, Elsevier, Elsevier, vol. 34(1), pages 14-30.
- Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & TÃ´, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, Elsevier, vol. 40(C), pages 989-1000.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.