September 22nd, 2020, 1:21 pm
To get the exact answer you’d need both models, but a reasonable approximation is found by dividing the H-L vol by the forward swap rate. E.g., if the forward swap rate is 1% and the H-L vol is 60 basis points, the corresponding Black vol is 60%. This works best for swaptions close to the money, and of course can fail catastrophically in the presence of negative rates.