# Implied volatility of inverse quote

Suppose I have a quote of INR/USD and the implied vol surface is also given. Is it theoritically correct to use to same implied vol for analysis of the inverse quote, i.e. USD/INR.

Correct me if I am wrong, but standard deviation of x and 1/x are not same.

• Correct me if I am wrong, but standard deviation of x and 1/x are not same: If x is lognormal, then SD(x) = SD(1/x). – byouness May 13 '18 at 20:48

The implied vol at strike $1/K$ and maturity $T$ for USDINR under the INR $T$-forward measure is the same than the implied vol at strike $K$ and maturity $T$ for INRUSD under the USD $T$-forward measure.