C'è da dire che alcuni miti sulla persistenza del premio al rischio della volatilità (VRP) si sciolgono come neve al sole nel momento in cui si esce da Black & Scholes e si usano formule "model free" che tengano conto dei momenti più alti della distribuzione.VIX Dropped Below S&P 500 Realized Volatility | Seeking Alpha
Historically, implied volatility tends to stay above realized volatility due to the skewed distribution of stock returns. It is "normal" when VIX is above the realized volatility of the broad equity market. The spread is usually around 3-4 points. It tended to narrow during periods of market turbulence; 2008 was the only year that average VIX readings, which were higher than usual, fell short of the realized volatility. On the contrary, while the 2017 VIX level was lower than usual, the relationship between implied and realized volatility remained fairly "normal." The negative spread between VIX and realized volatility reflects overall complacency in the market.
Why is implied volatility normally higher than realized? From a behavioral finance perspective, this is an indication of risk aversion - investors are willing to pay a premium to buy protection against risk. From an option pricing perspective, it is because stocks and stock indices do not follow the log-normal distribution assumption of Black-Scholes. The empirical distribution of stock returns has a negative skew and hence reflects larger losses than a normal or log-normal model using the ex-post mean and standard deviation would predict. Implied volatility takes into account large but rare events, while realized volatility will only include such events if they have occurred in the look-back calculation period. Since low-probability events are rare by definition, realized volatility tends to understate the potential for large losses most of the time. However, in a distressed market, realized volatility tends to overstate the risk of large losses when these sudden moves indeed occurred in the calculation window.
In effetti la volatilità storica è una misura molto povera per definire cosa potrebbe accadere di estremo al sottostante, da qui una buona fetta di VRP illusorio.