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 underlying asset has to be estimated for the life of the option.
The potential change in volatility tends to increase the value of options, notably of OTM contracts. Large price jumps have a specific effect. They tend to increase the relative value of OTM and ITM options, while decreasing the relative value of ATM contracts (when the jump is related to a specific security and not the overall market).
The many problems with the Black-Scholes formula do not negate the work it represents. However, it does point out the problems (especially relating to volatility) that traders face in trying to reconcile value and price. When the other variables and flawed assumptions are added in, the overall challenge for options traders is considerable. To use the formula effectively, it has to be accepted as only an approximation of a formula everyone could apply, if they knew how to take the variables into account.
Michael Thomsett blogs at the CBOE Options Hub and several other sites. He is author of 11 options books and has been trading options for 35 years. Thomsett Publishing Website
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