April 18th, 2015, 3:07 pm
There are at least a couple of ways to look at it. First you can inspect the SDEs: [$] dF=\mu_N dt + \sigma_N dW [$] vs [$] dF=\mu_L F dt + \sigma_L F dW[$]. Second, if you take the price of an at-the-money-forward swaption and back out implied volatilities from the standard Bachelier and Black models, you will find that, indeed, [$] \sigma_N \approx \sigma_L F [$].