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The Bias in Black-Scholes/Black Implied Volatility: An Analysis of Equity and Energy Markets

34 Pages Posted: 8 Dec 2004 Last revised: 7 Nov 2014

James Doran

Implied Capital Advisors

Ehud I. Ronn

University of Texas at Austin - Department of Finance

Abstract

In this paper we examine the extent of the bias between Black-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 and 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.

Keywords: Option pricing, volatility, energy, derivatives

Suggested Citation

Doran, James and Ronn, Ehud I., The Bias in Black-Scholes/Black Implied Volatility: An Analysis of Equity and Energy Markets. Review of Derivatives Research, Vol. 8, No. 3, 2005. Available at SSRN: https://ssrn.com/abstract=628722 or http://dx.doi.org/10.2139/ssrn.628722

James Doran (Contact Author)

Implied Capital Advisors ( email )

1942 Broadway Suite 409
Boulder, CO 80302
United States

Ehud Ronn

University of Texas at Austin - Department of Finance ( email )

Graduate School of Business
Austin, TX 78712
United States
512-471-5853 (Phone)
512-471-5073 (Fax)

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