Humps in the Volatility Structure of the Crude Oil Futures Market
This paper analyzes the volatility structure of commodity derivatives markets. The model encompasses stochastic volatility that may be unspanned by futures contracts. A generalized hump-shaped volatility specification is assumed that entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on commodity futures. An empirical study of the crude oil futures volatility structure is carried out using an extensive database of futures prices as well as futures option prices spanning 21 years. The study supports a hump-shaped, partially spanned stochastic volatility specification. Factor hedging, which takes into account shocks to both the volatility processes and the futures curve, depicts the presence of unspanned components in the volatility of commodity futures and the outperformance of the hump-shaped volatility in comparison to the more popular exponential decaying volatility. This hump shaped feature is more pronounced when the market is volatile.
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- Hilliard, Jimmy E. & Reis, Jorge, 1998. "Valuation of Commodity Futures and Options under Stochastic Convenience Yields, Interest Rates, and Jump Diffusions in the Spot," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(01), pages 61-86, March.
- Gibson, Rajna & Schwartz, Eduardo S, 1990. " Stochastic Convenience Yield and the Pricing of Oil Contingent Claims," Journal of Finance, American Finance Association, vol. 45(3), pages 959-76, July.
- Carl Chiarella & Oh Kang Kwon, 2001.
"Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model,"
Finance and Stochastics,
Springer, vol. 5(2), pages 237-257.
- Carl Chiarella & Oh-Kang Kwon, 1999. "Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model," Research Paper Series 5, Quantitative Finance Research Centre, University of Technology, Sydney.
- Darrell Duffie & Rui Kan, 1996. "A Yield-Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406.
- Bekaert, Geert & Hodrick, Robert J. & Marshall, David A., 2001.
"Peso problem explanations for term structure anomalies,"
Journal of Monetary Economics,
Elsevier, vol. 48(2), pages 241-270, October.
- Geert Bekaert & Robert J. Hodrick & David A. Marshall, 1997. ""Peso Problem" Explanations for Term Structure Anomalies," NBER Working Papers 6147, National Bureau of Economic Research, Inc.
- Geert Bekaert & Robert J. Hodrick & David A. Marshall, 1997. ""Peso problem" explanations for term structure anomalies," Working Paper Series, Issues in Financial Regulation WP-97-07, Federal Reserve Bank of Chicago.
- 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.
- Mark Broadie & Mikhail Chernov & Michael Johannes, 2009.
"Understanding Index Option Returns,"
Review of Financial Studies,
Society for Financial Studies, vol. 22(11), pages 4493-4529, November.
- Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Bekiros, S. & Diks, C.G.H., 2007.
"The Relationship between Crude Oil Spot and Futures Prices: Cointegration, Linear and Nonlinear Causality,"
CeNDEF Working Papers
07-11, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
- Bekiros, Stelios D. & Diks, Cees G.H., 2008. "The relationship between crude oil spot and futures prices: Cointegration, linear and nonlinear causality," Energy Economics, Elsevier, vol. 30(5), pages 2673-2685, September.
- K. R. Miltersen, 2003. "Commodity price modelling that matches current observables: a new approach," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 51-58.
- Leif Andersen, 2010. "Markov models for commodity futures: theory and practice," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 831-854.
- Miltersen, Kristian R. & Schwartz, Eduardo S., 1998. "Pricing of Options on Commodity Futures with Stochastic Term Structures of Convenience Yields and Interest Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(01), pages 33-59, March.
- Doran, James S. & Ronn, Ehud I., 2008. "Computing the market price of volatility risk in the energy commodity markets," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2541-2552, December.
- Litzenberger, Robert H & Rabinowitz, Nir, 1995. " Backwardation in Oil Futures Markets: Theory and Empirical Evidence," Journal of Finance, American Finance Association, vol. 50(5), pages 1517-45, December.
- Rong Fan & Anurag Gupta & Peter Ritchken, 2003. "Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets," Journal of Finance, American Finance Association, vol. 58(5), pages 2219-2248, October.
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