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As opposed to the received wisdom of the random walk model, most investment vehicles sport different volatilities over different time horizons. Volatility is especially high when both supply and demand are inelastic and liable to large, random shocks. This is why the prices of industrial goods are less volatile than the prices of shares, or commodities.
Last month, in the Paris congress, Douglas Breeden, dean of Duke University's Fuqua School of Business, warned that to quote from the same issue of Risk Magazine: " 'Estimation risk' plagues even the best-designed risk management system. Firms must estimate risk and return parameters such as means, betas, durations, volatilities and convexities, and the estimates are subject to error.
The folly of this argument lies in the fact that stochastic volatility contradicts the assumption required by the B-S model if volatilities do change stochastically through time, the Black-Scholes formula is no longer the correct pricing formula and an implied volatility derived from the Black-Scholes formula provides no new information."
Black-Scholes is thought deficient on other issues as well. The implied volatilities of different options on the same stock tend to vary, defying the formula's postulate that a single stock can be associated with only one value of implied volatility. The model assumes a certain geometric Brownian distribution of stock prices that has been shown to not apply to US markets, among others.
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