Implied Volatility Bias

[benzbubblecat]

T/F & why:

In retrospect, the volatility implied by Black-Scholes shows an upward bias versus realized volatility. This is because BS assumes that the distribution of returns is normal, which it usually isn't. (if this is true, how can we correct for this in the model?)

 

[Brad Warren]

The volatility skew is a well-known phenomon indicating the market does not believe that returns are lognormal. The BS implied vol is just the wrong number you put in the wrong formula to give you the "right" (market) price. Attempts to address the limitations of Black-Scholes include stochastic and local volatility models.

 

[financeguy]

T/F & why:

In retrospect, the volatility implied by Black-Scholes shows an upward bias versus realized volatility. This is because BS assumes that the distribution of returns is normal, which it usually isn't. (if this is true, how can we correct for this in the model?)

1) future includes uncertainty while historics don't
2) implied probability distribution is not normal - so a smile exists to reflect that, and ATM vol wont be an absolute direct comparison to the historical normal standard distribution of returns
3) would you sell anything for less than it has been worth in the recent past? extreme cases exist, but generally i wouldnt