Review of Derivatives Research

, Volume 8, Issue 3, pp 177–198 | Cite as

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



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.


Implied volatility Energy markets Black-Scholes 


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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of FinanceCollege of Business, Florida State UniversityTallahasseeUSA
  2. 2.Department of Finance, McCombs School of BusinessUniversity of Texas at AustinAustinUSA

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