What implied volatility skew is

If the assumptions behind the Black-Scholes model held exactly, every strike on one expiration would imply the same volatility, and a plot of implied volatility against strike would be a flat line. It is not flat. For US equity and index options it slopes downward as the strike rises: puts below the forward imply more volatility than calls above it.

The usual explanation is that returns are not symmetric. Large downward moves arrive faster and cluster more than large upward ones, and holders of equity purchase downside protection persistently. Both push the price of low-strike options above what a symmetric model would charge, and implied volatility is where that shows up.

Two summary numbers do most of the work. The 25-delta risk reversal is the implied volatility of the 25-delta put minus that of the 25-delta call. It is quoted in volatility points, and for equities it is normally positive. The 25-delta butterfly is the average of those two wings minus the at-the-money reading, which describes how curved the smile is rather than how tilted.

Both are read off a curve fitted through the surviving quotes, at the delta rather than at a fixed strike. Delta moves with volatility and time, so a fixed strike would mean something different from one session to the next while a fixed delta does not.

Moneyness and delta are both measured against the forward price, not the last traded price of the underlying. The forward is derived from put-call parity on the strikes nearest the money.

Substituting the underlying close for the forward is the most common way a skew reading goes wrong. The close embeds neither the dividend nor the cost of borrowing the stock, so in a hard-to-borrow name the whole curve shifts in moneyness terms and the risk reversal picks up a bias that looks exactly like real demand for puts.