  Vanna-Volga is a popular method for the interpolation/extrapolation of
volatility smiles. The technique is widely used in the FX markets context, due
to its ability to consistently construct the entire Lognormal smile using only
three Lognormal market quotes. However, the derivation of the Vanna-Volga
method itself is free of distributional assumptions. With this is mind, it is
surprising there have been no attempts to apply the method to Normal
volatilities (the current standard for interest rate markets). We show how the
method can be modified to build Normal volatility smiles. As it turns out, only
minor modifications are required compared to the Lognormal case. Moreover, as
the inversion of Normal volatilities from option prices is easier in the Normal
case, the smile construction can occur at a machine-precision level using
analytical formulae, making the approximations via Taylor-series unnecessary.
Apart from being based on practical and intuitive hedging arguments, the
Vanna-Volga has further important advantages. In comparison to the Normal SABR
model, the Vanna-Volga can easily fit both classical convex and atypical
concave smiles (frowns). Concave smile patterns are sometimes observed around
ATM strikes in the interest rate markets, particularly in the situations of
anticipated jumps (with an unclear outcome) in interest rates. Besides,
concavity is often observed towards the lower/left end of the Normal volatility
smiles of interest rates. At least in these situations, the Vanna-Volga can be
expected to interpolate/extrapolate better than SABR.
