Black-Scholes：為何關註波動性？

My own opinion is that people are too bemused by the famous cancellation of $\mu$ in the BS pde. After all, that's what impressed the Nobel Prize committee, so it must be right. But both Black & Schole's original derivation using asset pricing theory and Merton's later self-financing portfolio argument are enormous over-simplifications of the real world, and contra the Sveriges Rijksbank, Black, Scholes, & Merton did not show that "... it is in fact not necessary to use any risk premium when valuing an option".

最佳答案

• Implied Volatility (IV) is the input to any vanilla option pricing model (not just Black Scholes (BS) that impacts the pricing the most. You can verify this by flipping through the different risk exposures (greeks and higher order sensitivities) and study mean volatilities in such risk factors and their impact on the pricing of such options.

• Traders who price and buy/sell options in effect trade future realized volatility/expected variation in the underlying asset returns. Hence, option traders express views on such future asset price variation and thus buy and sell volatility. The term "implied" volatility is in my opinion a bit of a misnomer because the trade starts with an agreed level of volatility and not an option price.

(In fact, you hardly ever hear any professional traders agreeing on an option price, they most often agree on the exact implied vols they trade at, and often times also trade the delta alongside the option (at least in equity space) in order to have the option delta-hedged at initiation.)

Option pricing models are used to translate the expressed IV -> Price. When you see option prices on your trading screen then those are the outputs of automated pricing applications which as input take among couple other mostly statics, IV.

EDIT:

I highly recommend to go through the following short paper: Option Pricing Q&A