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The bias in Black-Scholes/Black implied volatility: an analysis of equity and energy markets. (English) Zbl 1201.91210
Summary: 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.

MSC:
91G30 Interest rates, asset pricing, etc. (stochastic models)
91B24 Microeconomic theory (price theory and economic markets)
91G80 Financial applications of other theories
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