FX Delta

In FX world, we have a delta similar greek to measure foreign exposure - PnL change for a shift of 1% of the spot for outstanding foreign positions. Which turn out nothing but the discounted notional, below is the derivation. $$F = S * e^{r_f - r_d}$$ $$F * N = S * e^{r_f - r_d} * N $$ $$FX-Delta = \frac{\partial F}{\partial S} = \frac{(S * 1.01 - S) * e^{r_f - r_d} * N}{S * 1.01 - S} = e^{r_f - r_d} * N$$