On a FX volatility smile, Is a-delta put volatility equal to (1-a)-delta call volatility?

Question

On a FX volatility smile in terms of delta, If I want 95-delta put vol, Is this volatility equal to a 5-delta call vol, and viceversa?

Thanks.

Answer 1

It depends on the delta convention. The parity $$ \Delta_{\text{Put}(\text{strike } K)} = 1 - \Delta_{\text{Call}(\text{strike } K)} $$ works only when the delta convention is forward delta, so the 95-delta put vol is equal to the 5-delta call vol only in this case.

See Reiswich & Wystup FX Volatility Smile Construction for a list of all delta conventions and how to build the corresponding strikes. For most markets (e.g. EURUSD, ...) the delta convention is spot delta until 1Y, and forward delta over 1Y.