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The bias in Black-Scholes/Black implied volatility: An analysis of equity and energy markets

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  • James Doran
  • Ehud Ronn

Abstract

In this paper we examine the extent of the bias between Black and Scholes (1973)/Black (1976) implied volatility and realized term volatility in the equity and energy markets. Explicitly modeling a market price of volatility risk, we extend previous work by demonstrating that Black-Scholes is an upward-biased predictor of future realized volatility in S&P 500/S&P 100 stock-market indices. Turning to the Black options-on-futures formula, we apply our methodology to options on energy contracts, a market in which crises are characterized by a positive correlation between price-returns and volatilities: After controlling for both term-structure and seasonality effects, our theoretical and empirical findings suggest a similar upward bias in the volatility implied in energy options contracts. We show the bias in both Black-Scholes/Black implied volatilities to be related to a negative market price of volatility risk. Copyright Springer Science+Business Media, LLC 2005

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  • 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.
    • Handle: RePEc:kap:revdev:v:8:y:2005:i:3:p:177-198
    DOI: 10.1007/s11147-006-9002-2
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    3. Algieri, Bernardina & Leccadito, Arturo & Tunaru, Diana, 2021. "Risk premia in electricity derivatives markets," Energy Economics, Elsevier, vol. 100(C).
    4. Banerjee, Prithviraj S. & Doran, James S. & Peterson, David R., 2007. "Implied volatility and future portfolio returns," Journal of Banking & Finance, Elsevier, vol. 31(10), pages 3183-3199, October.
    5. Luo, Xingguo & Ye, Zinan, 2015. "Predicting volatility of the Shanghai silver futures market: What is the role of the U.S. options market?," Finance Research Letters, Elsevier, vol. 15(C), pages 68-77.
    6. Gomes, Frederico Pechir & Takami, Marcelo Yoshio & Brandi, Vinicius Ratton, 2008. "Investigating Unusual Changes in Real-Dollar Exchange Rate," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 62(2), October.
    7. Haugom, Erik & Langeland, Henrik & Molnár, Peter & Westgaard, Sjur, 2014. "Forecasting volatility of the U.S. oil market," Journal of Banking & Finance, Elsevier, vol. 47(C), pages 1-14.
    8. Liu, Zhichao & Ma, Feng & Long, Yujia, 2015. "High and low or close to close prices? Evidence from the multifractal volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 50-61.
    9. Arismendi, Juan C. & Back, Janis & Prokopczuk, Marcel & Paschke, Raphael & Rudolf, Markus, 2016. "Seasonal Stochastic Volatility: Implications for the pricing of commodity options," Journal of Banking & Finance, Elsevier, vol. 66(C), pages 53-65.
    10. Roncoroni, Andrea & Prokopczuk, Marcel & Ronn, Ehud I., 2018. "Introduction—special issue on commodity and energy markets in the Journal of Banking and Finance," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 1-4.
    11. Andy Fodor & James S. Doran & James M. Carson & David P. Kirch, 2013. "On the Demand for Portfolio Insurance," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 16(2), pages 167-193, September.
    12. Chatrath, Arjun & Miao, Hong & Ramchander, Sanjay, 2014. "Crude oil moments and PNG stock returns," Energy Economics, Elsevier, vol. 44(C), pages 222-235.
    13. Libo Yin, 2022. "The role of intermediary capital risk in predicting oil volatility," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 401-416, January.
    14. 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.
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    16. Gatfaoui, Hayette, 2013. "Translating financial integration into correlation risk: A weekly reporting's viewpoint for the volatility behavior of stock markets," Economic Modelling, Elsevier, vol. 30(C), pages 776-791.

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