Computing the market price of volatility risk in the energy commodity markets
AbstractIn this paper, we demonstrate the need for a negative market price of volatility risk to recover the difference between Black-Scholes [Black, F., Scholes, M., 1973. The pricing of options and corporate liabilities. Journal of Political Economy 81, 637-654]/Black [Black, F., 1976. Studies of stock price volatility changes. In: Proceedings of the 1976 Meetings of the Business and Economics Statistics Section, American Statistical Association, pp. 177-181] implied volatility and realized-term volatility. Initially, using quasi-Monte Carlo simulation, we demonstrate numerically that a negative market price of volatility risk is the key risk premium in explaining the disparity between risk-neutral and statistical volatility in both equity and commodity-energy markets. This is robust to multiple specifications that also incorporate jumps. Next, using futures and options data from natural gas, heating oil and crude oil contracts over a 10Â year period, we estimate the volatility risk premium and demonstrate that the premium is negative and significant for all three commodities. Additionally, there appear distinct seasonality patterns for natural gas and heating oil, where winter/withdrawal months have higher volatility risk premiums. Computing such a negative market price of volatility risk highlights the importance of volatility risk in understanding priced volatility in these financial markets.
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): 12 (December)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jbf
Volatility risk premium Energy futures and options markets;
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.:
- Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, 06.
- French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 2000.
"Transform Analysis and Asset Pricing for Affine Jump-Diffusions,"
Econometric Society, vol. 68(6), pages 1343-1376, November.
- Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.
- 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.
- Eduardo Schwartz & James E. Smith, 2000. "Short-Term Variations and Long-Term Dynamics in Commodity Prices," Management Science, INFORMS, vol. 46(7), pages 893-911, July.
- Hentschel, Ludger, 2003. "Errors in Implied Volatility Estimation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(04), pages 779-810, December.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
- Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- Joshua D. Coval, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, 06.
- Bryan Routledge & Duane Seppi & Chester Spatt, .
"Equilibrium Forward Curves for Commodities,"
GSIA Working Papers
1997-49, Carnegie Mellon University, Tepper School of Business.
- Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
- Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
- Robert S. Pindyck, 1999.
"The Long-Run Evolutions of Energy Prices,"
The Energy Journal,
International Association for Energy Economics, vol. 0(Number 2), pages 1-27.
- Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
- Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
- 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.
- Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, EconWPA.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
- Yacine Ait-Sahalia, 1995.
"Nonparametric Pricing of Interest Rate Derivative Securities,"
NBER Working Papers
5345, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
- Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, 06.
- Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
- Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
- Jones, Christopher S., 2003. "The dynamics of stochastic volatility: evidence from underlying and options markets," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 181-224.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
- Narayan, Paresh Kumar & Sharma, Susan Sunila, 2011. "New evidence on oil price and firm returns," Journal of Banking & Finance, Elsevier, vol. 35(12), pages 3253-3262.
- Ramos, Sofia B. & Veiga, Helena, 2011.
"Risk factors in oil and gas industry returns: International evidence,"
Elsevier, vol. 33(3), pages 525-542, May.
- Sofía B. Ramos & Helena Veiga, 2009. "Risk factors in oil and gas industry returns: international evidence," Statistics and Econometrics Working Papers ws096920, Universidad Carlos III, Departamento de Estadística y Econometría.
- Kellard, Neil & Dunis, Christian & Sarantis, Nicholas, 2010. "Foreign exchange, fractional cointegration and the implied-realized volatility relation," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 882-891, April.
- Paschke, Raphael & Prokopczuk, Marcel, 2010. "Commodity derivatives valuation with autoregressive and moving average components in the price dynamics," Journal of Banking & Finance, Elsevier, vol. 34(11), pages 2742-2752, November.
- Sévi, Benoît & Chevallier, Julien, 2013.
"A Fear Index to Predict Oil Futures Returns,"
Economics Papers from University Paris Dauphine
123456789/11714, Paris Dauphine University.
- Back, Janis & Prokopczuk, Marcel & Rudolf, Markus, 2013. "Seasonality and the valuation of commodity options," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 273-290.
- repec:wyi:wpaper:002038 is not listed on IDEAS
- repec:wyi:wpaper:002033 is not listed on IDEAS
- Carl Chiarella & Boda Kang & Christina Nikitopoulos-Sklibosios & Thuy-Duong To, 2012. "Humps in the Volatility Structure of the Crude Oil Futures Market," Research Paper Series 308, Quantitative Finance Research Centre, University of Technology, Sydney.
- Cheong, Chin Wen, 2009. "Modeling and forecasting crude oil markets using ARCH-type models," Energy Policy, Elsevier, vol. 37(6), pages 2346-2355, June.
- Anders B. Trolle & Eduardo S. Schwartz, 2009. "Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4423-4461, November.
- Cameron, Ken & Schnusenberg, Oliver, 2009. "Oil prices, SUVs, and Iraq: An investigation of automobile manufacturer oil price sensitivity," Energy Economics, Elsevier, vol. 31(3), pages 375-381, May.
- James Doran & Ehud Ronn, 2005. "The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets," Review of Derivatives Research, Springer, vol. 8(3), pages 177-198, December.
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.