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Further thoughts on the shortcomings of the Black-Scholes pricing model:

Three possible causes (separately or together) for differences between value and price related to volatility are: (1) the value is correct but the option price is not; (2) the incorrect outputs are derived from the Black-Scholes model; and (3) the Black-Scholes model might be inaccurate.

The primary cause of inaccuracy is due to the underlying assumption that volatility is a constant. This means that volatility of the underly

The original Black-Scholes formula often is cited as the authoritative source for options pricing. However, with a large number of variables built into option formulae, it is surprising that they occasionally are close to approximating or matching market value.

The Black-Scholes formula as originally published was full of unrealistic assumptions. These include:

1. Volatility is fixed and never changes.

2. The short-term interest rate never changes.

3. Anyone can lend or borrow as much as he wants as