Suppose you are given the whole volatility smile shape as a function of strikesFormulas to retrieve RR and Butterfly areRR 25D = 25 D Call Vol - 25 D Put volFly 25D = (25 D Call Vol + 25 D Put Vol ) /2 - ATM VolBut I'm not sure what "25 delta" actually means.From what I understand, 25D for the risky refers to: the vol at the strike where smile delta = 25 (not black scholes delta)The computation for the BF seems even more complicatedi'm lost... can anyone explain please?

Hi quantstudent19,I am not an expert, but my understanding is that for a given expiration t* you solve for StrikeCall [with VolCall(StrikeCall) specified] such that DeltaCall = 0.25, and similarly you solve for StrikePut [with VolPut(StrikePut) specified] such that DeltaPut = -0.25 . These numbers with smile, VolCall and VolPut, are used in the risk reversal RR 25D. It would be logical that these same numbers would be used in any other expression like the Fly 25D, although I don’t know that for a fact.To get the deltas, you use the option prices with smile, i.e. Call(FXspot,VolCall, StrikeCall), Put(FXspot,VolPut, StrikePut), again with VolCall(StrikeCall), VolPut(StrikePut) specified by the smile. ---------

QuoteOriginally posted by: quantstudent19Suppose you are given the whole volatility smile shape as a function of strikesFormulas to retrieve RR and Butterfly areRR 25D = 25 D Call Vol - 25 D Put volFly 25D = (25 D Call Vol + 25 D Put Vol ) /2 - ATM VolBut I'm not sure what "25 delta" actually means.From what I understand, 25D for the risky refers to: the vol at the strike where smile delta = 25 (not black scholes delta)The computation for the BF seems even more complicatedi'm lost... can anyone explain please?okay typically you do the reverse from the market you have apart from ATM, quotes on RR, STR at 10,25,75,90 deltas and from that you obtain the 10,25,75,90 delta vols. And for a new option with say 30delta you can interpolate with your favorite functional form!

i guess my question isnt clear enough in my mindthank you all for your answersi might come back later

25 delta = out of the money option (0.25/OTM ; 0.5/ATM; 0.75/ITM)it is preferable to quote delta as a measure for 100 op...so.. 0.25 (1 call out the money)*100the RR 25d gives u the simmetry of the smile; the Fly 25 gives u the curvature

In addition, note that for FX, the Call/Put is on the first currency (quoted in BB convention).Call USD / JPY => Call on USDCall EUR / USD => Call on EURAlso, the vol smile is qouted as [e.g. Bloomberg OVDV screen]10 Delta Call, 25 Delta Call, ATM, 25 Delta Put, 10 Delta PutHere, 25D Put = 75D Call; 10D Put = 90D Call.