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

Authors: Doran, James¹; Ronn, Ehud²

Source: Review of Derivatives Research, Volume 8, Number 3, December 2005 , pp. 177-198(22)

Publisher: Springer

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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.

Keywords: Implied volatility; Energy markets; Black-Scholes

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s11147-006-9002-2

Affiliations: 1: Email: jsdoran@cob.fsu.edu 2: Email: eronn@mail.utexas.edu

Publication date: 2005-12-01