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Hi,I am trying to make an FX vol surface.I have the following data at discrete intervals for a range of tenors.Spot priceForward prices (swap rates)ATM implied vol25 delta and 10 delta butterfly vol (given as the spread above / below spot)25 delta and 10 delta risk reversal vol (given as the spread above / below spot)I found a note which read as follows:The formula for constructing the smile (for a given delta) isP = ATM + BFLY - .5 * RRC = ATM + BFLY + .5 * RREx. for midrate EURUSD 1w volatilities (see also attached screenshot)P = 7.35 + .25 - .5 * .1 = 7.55C = 7.35 + .25 + .5 * .1 = 7.65But the problem is that it doesn't tell me how to get the implied vol for a given strike (or delta).Do I interpolate (using a cubic spleen or linear or whatever) the Butterfly and RR? for the strike I want to get the vol for? In short... how do I get a vol surface using the given data?Thank you for your help!N

nmaughan, there are atleast 5 previous threads on this topic which discuss this in great detail, just search a bit. amit7ul

I did some searching before posting. If you would be so kind as to reference them I would be grateful.

I'm guessing most of the threads on this topic cover the bit that you had - from those formulas you can get the vol for a 10 and 25 delta call, put, and ATM.Once you've got the vol for those 5 points, there is no set rule as to how you fit the rest of the curve - cubic spline is probably as good as most.

Thank you for your responses.Please allow me to clarify my question, I feel that I may not have made it sufficiently explicit.In order to calculate the vol for a given delta would one simply interpolate between the butterfly and risk reversal points given and then use the interpolated values in the formula in my first post on this subject? Also, ought one use the ATM vol 'as is' or is any alteration required to the ATM vol across deltas (if so, what?).For example, if:10 delta Butterfly = 1% (over ATM)25 delta Butterfly = 2% (over ATM)10 delta risk reversal = 0.5% (over ATM)25 delta risk reversal = 1.25% (over ATM)1 week forward price = 1.8500ATM vol = 12%and we wish to calculate the 25 delta call vol then would this be: 12%+2%+0.5*1.25% = 14.63% ?Further, assume that we use a linear interpolation for simplicity in this example and we wish to price the 17.5 delta call (so that we can keep it simple and use equal weightings for the interpolation); would this be as follows?12%+((0.5*2%)+(0.5*1%))+0.5*((0.5*1.25%)+(0.5*0.5%))=13.94%If this is the case and one simply ought to interpolate between the 10 and 25 delta points for the RR and FLY then how does one calculate a vol for deltas below 10 or above 25 with only these data points?I guess that to get vols above 25d but below 50 one could calculate that for 25 and interpolate between there and ATM... is there any other way that I am blindly missing?If anyone can tell me if I am on the right track here or if I am way off I would be very grateful.Thank you.N

Any thoughts?