Unobservable volatility means the Black-Scholes-Merton model has no unique predicted price.

Evidence

Certainly one should not underestimate the complexity of judging whether patterns of market prices, for example, have moved toward greater conformity with a model such as Black-Scholes-Merton. One way of formulating the question is to examine the extent to which the model’s predictions are borne out. However, what a model predicts is often not straightforward. The BlackScholes-Merton model, for example, yields an option price only after the characteristics of the option and the values of the parameters of the Black-Scholes equation have been set. One parameter, the volatility of the stock, is acknowledged not to be directly observable, so there is no unique theoretical price to compare with “actual” prices. — Donald MacKenzie, An Engine, Not a Camera, 102

Categorization

• XREF: Connects to the known ‘volatility smile’ critique of Black-Scholes and the implied-volatility inversion used in practice. — connects to: The Black-Scholes formula contains no risk parameter, implying risk-neutral pricing. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 598; The Black-Scholes equation excludes expected returns and risk aversion entirely — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 610; Economists favored Black-Scholes-Merton for its minimal unobservable parameters and efficient-market grounding. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 724
• DEFINE: Explains why testing a financial model against market prices is underdetermined when a key parameter is unobservable.

Broader Connections

• The Black-Scholes formula contains no risk parameter, implying risk-neutral pricing. #expands (0.85) — Donald MacKenzie, An Engine, Not a Camera, 598
• The Black-Scholes equation excludes expected returns and risk aversion entirely #expands (0.85) — Donald MacKenzie, An Engine, Not a Camera, 610