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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.
Studies have exposed serious departures from the price process
fundamental to Black-Scholes: skewness, excess kurtosis (i.e.,
concentration of prices around the mean), serial correlation, and time
varying volatilities. Black-Scholes tackles stochastic volatility
poorly.
The formula also unrealistically assumes that the market dickers
continuously, ignoring transaction costs and institutional constraints.
No wonder that traders use Black-Scholes as a heuristic rather than a
price-setting formula.
Volatility also decreases in administered markets and over different
spans of time. 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.
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