neftci
If this Black-Scholes assumption is violated, wouldn’t the price given by the Black-Scholes
formula be “wrong,” and, hence, the volatility implied by the formula be erroneous? This question
needs to be carefully considered. In the end, we will see that there really are no inconsistencies
in traders’ behavior.We can explain this as follows.
1. First, note that the Black-Scholes formula is simple and depends on a small number
of parameters. In fact, the only major parameter that it depends on is the volatility, σ.
Asimple formula has some advantages. It is easy to understand and remember. But, more
importantly, it is also easy to realize where or when it may go wrong. A simple formula
permits developing ways to correct for any inaccuracies informally by making subjective
adjustments during trading. The Black-Scholes formula has one parameter, and it may be
easier to remember how to “adjust” this parameter to cover for the imperfections of the
formula.11
2. An important aspect of the Black-Scholes formula is that it has become a convention.
In other words, it has become a standard among professionals and also in computer
platforms. The formula provides a way to connect a volatility quote to a dollar value
attached to this quote. This way traders use the same formula to put a dollar value on a
volatility number quoted by the market. This helps in developing common platforms for
hedging, risk managing, and trading volatility.
3. Thus, once we accept that the use of the Black-Scholes formula amounts to a convention,
and that traders differ in their selection of the value of the parameter σ, then the critical
process is no longer the option price, but the volatility. This is one reason why in many
markets, such as caps, floors, and swaptions markets, the volatility is quoted directly.

而是问假设B-S公式的应用条件成立，B-S算出的价格是不是理论上的期权费？
理论上的期权费不就是这个诺奖公式推出来的么？还是我没理解这个问题。
我还是认为对波动率的理解加深后，对期权的理论价和市场价会有更好的理解。