Why is Implied Volatility more important than skew for put spread pricing?

Question

It is said on page 26 of the book "Trading Volatility: Trading Volatility, Correlation, Term Structure and Skew" by Bennett (2014) that:

A rule of thumb is that the value of the OTM put sold should be approximately one-third the value of the long put (if it were significantly less, the cost saving in moving from a put to a put spread would not compensate for giving up complete protection). While selling an OTM put against a near-ATM put does benefit from selling skew (as the implied volatility of the OTM put sold is higher than the volatility of the near ATM long put bought), the effect of skew on put spread pricing is not normally that significant (far more significant is the level of implied volatility).

So basically, not only skew is needed, but it should be highly skewed? Is that what this means?

Isn't skew and IV similar in nature?

Answer 1

All that is saying is that the level of the implied volatility curve is more important than the slope (which is more important than the curvature) when it comes to pricing these spreads.

For argument's sake, let's take the 90/85 % put spread (long 90, short 85) with s = 100, $\sigma_{90} = 20$%, $\sigma_{85} = 21$%, $r=0, T = 1$. With these initial values, the put spread's value is 1.16. If we bump the overall IV curve by 10% to 30% and 31% for the 90 and 85 strikes respectively, the new value is 1.60.

If we bump the skew between the 90 and 85 strikes higher, to a 2% spread, the value at ~20% IV is 0.89 (a 0.27 discount), and at ~30% IV it's 1.29 (a 0.31 discount).

Since the changes in IVs of different strikes are assumed to be positively correlated (i.e if the ATM vol rises, so to do the wing IVs), the level of IV is more volatile than the spread between different strikes.

Just as the order of importance for pricing options goes: Level -> Slope -> Curvature (in order of the derivative), the same goes for other areas in finance, like bond prices, where the overall curve level is most volatile, then the spread between terms, then the curvature of term structure.

Answer 2

The text just means they use that their "rule of thumb" to sell options with higher volatility than options with lower volatiliy (the skew element of puts), but also satisfying that price condition of OTM options not being less than a third of an ATM option.