  First, we show that implied normal volatility is intimately linked with the
incomplete Gamma function. Then, we deduce an expansion on implied normal
volatility in terms of the time-value of a European call option. Then, we
formulate an equivalence between the implied normal volatility and the
lognormal implied volatility with any strike and any model. This generalizes a
known result for the SABR model. Finally, we adress the issue of the "breakeven
move" of a delta-hedged portfolio.
