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

*James Doran* () and
*Ehud Ronn* ()

*Review of Derivatives Research*, 2005, vol. 8, issue 3, 177-198

**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

**Keywords:** Implied volatility; Energy markets; Black-Scholes (search for similar items in EconPapers)

**Date:** 2005

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**Persistent link:** https://EconPapers.repec.org/RePEc:kap:revdev:v:8:y:2005:i:3:p:177-198

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**DOI:** 10.1007/s11147-006-9002-2

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