+25/-25 delta call/put

Say ABC is trading at 100 $, which strikes would be the 25 delta call and -25 delta put.
Thanks for any responces

 

theres no simple way to answer that question... if the stock trades in a range of .10 cents a year.. then the 110 call is going to have an ultra low delta.. if the stock trades is very very volatile.. 110 strike could theoretically have a delta of 45... just for the sake of speaking as well.. time to expiration changes the delta of a strike .. the closer to expiration the farther otm an otm option becomes.. so there is no way to answer your question...

 

The strikes where the OTM options are 25% delta. I know it sounds unhelpful, but it IS the answer.

 

Ok , thanks
I found an article where the autor suggests that looking at the 25 delta call/put is a good way of illustrating the vol skew. What should I be looking at, the price or the IV of an option.

 

I would use the IV (call IV minus put IV).

 

Not the price that's for sure...

As a specific example, in FX people commonly look at two measures to characterize the skew: 1) the (25D) risk reversal, which is the difference between the OTM call and put vols (most commonly, using 25 delta options); and 2) the (25D) butterfly, which is computed as average(OTM call vol + OTM put vol) - ATMF vol (again, using the 25 delta options).

 

Ok thanks
It must be the same for equity and index options.

 

Not really. Equity and equity index vols, in general, are sticky strike volatility while FX is almost always sticky delta volatility. So, this leads to two things:

-- in the equity world it makes more sense to look at the difference between fixed % strike vols as the indicator of the skew. For example, you can use the SK10 = (Vol(ATM) - Vol(ATM-10%))/sqrt(TimeExpiry)).

-- risk-reversal (i.e. 25 delta put vol minus 25 delta call vol) is going to be a bad indicator of the richness of the skew since the distance between implied delta strikes is going to change as a function of the ATM volatility. E.g. 25RR in october of 2008 was much narrower (not wider!!!) then it is right now. Instead, you want to look at risk-reversal normalized by ATM vol, e.g. RRN = ( Vol(25d put) - Vol(25d call) )/Vol(50d).

-- SK10 one is better to use if you care about a specific asset, e.g. S&P500 since it's consistent across the expirations. RRN is better to use if you comparing skews across assets, e.g. comparing skew in S&P500 against skew in Russell 2000.

 

SK10 = (Vol(ATM) - Vol(ATM-10%))/sqrt(TimeExpiry)).

here your looking at the vol differential relative to the atm vol normalized by the time to expiration... if i hear you correctly..? so this way you can look at skew across expirations in the same asset and see that as you say its consistant across the calender..?? do i hear you correctly?

 

SLE, thank you for providing this very valuable perspective. I have only been modeling the 10RRs and 25RRs across expirations but will begin using these as well.