Measuring Options Skew with Risk Reversals and Delta Comparisons

# Calculating skew for an options structure


# Calculating skew for an options structure












I am trying to figure out whether an options structure is short or long skew without just having someone tell me the answer. I'd like to calculate the number myself. Assuming I am creating a risk reversal at strike 90, 110:

- for strike 110: skew = IV of call @ strike 110 - IV of call @ strike 111

- for strike 90: skew = IV of put @ strike 90- IV of put @ strike 91

- Skew for the risk reversal = -1x skew of call + 1x skew of put

Does this make sense?

## Answer by Frido (score 6, accepted)

https://quant.stackexchange.com/a/75785

There are many definitions / concepts of skew. For a good overview of 'skew' you might like Mixon, What does implied volatility skew measure?

What you have done in your example is calculate the slope of the implied volatility smile/skew at two different strikes and then compared the slopes at these two different points. Mathematically speaking there's nothing wrong with this, but that's not the usual way to trade skew or even to quantify skew.

The most straightforward way to trade skew is to trade a risk reversal, i.e. long an OTM put and short an OTM call. You'll be long skew then because if the skew increases, i.e. OTM put IVs increase and OTM call IVs decrease, your structure will gain in value if you bought the risk reversal, all else equal.

The devil is in the 'all else equal'.

The cleanest way to trade skew is actually to trade skewness, which is the third (central) moment of the underlying. But for this you'll need a strip of options appropriately weighted. Skewness is not skew as traders understand it though.

To really trade the difference between two implied volatilities without the other 'noise' you have to trade forward start implied vols of certain strikes; this will give you almost pure exposure to forward start skew, but that may be a step too far at this moment.

## Answer by RF OptionsManagement (score 0)

https://quant.stackexchange.com/a/85599

Using two OTM strikes, you are trying to measure skew, but in practice you are mostly picking up curvature effects.

You are effectively mixing slope (skew) and curvature (kurtosis).

A skew can be approximated between any two strikes, but if both are far from the ATM, the estimate becomes contaminated by curvature effects, since the volatility surface is not linear in the tails.

That is why skew is typically measured relative to the ATM or using symmetric delta constructions, such as Risk Reversals, which better isolate asymmetry rather than tail thickness.

When you calculate strike 110 – 111, you are not measuring skew, but emphasizing kurtosis.

To evaluate the implied distribution, it could be interesting, although deltas above 85 and below 15 usually tend to be mispriced.

For skew calculation, it makes more sense to use:

Calls: Strike 110 – Strike Delta 50 (I assume strike 100 would be D50 here)

Puts: Strike 90 – Strike Delta 50 Then you compare the difference

You could also go

*Call-Put skew: 110 Call – 90 Put, normalized by ATM IV.

*Risk Reversal: Call 25 – Put 25

*Call Skew: Call 75 – Call 25

*Put Skew: Put 75 – Put 25

You can always normalize by Delta 50.

Often, you will not find in the options chains strikes that exactly mathc the deltas 25, 50, 75. In this case, you must interpolate the volatility curve in order to get the exact deltas.