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tetoche
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Ho-Lee Vol to Black Vol

September 22nd, 2020, 8:59 am

Hi
Is there a simple mean to transform Ho-Lee volatility to Black volatility for swaption pricing?
 
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bearish
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Re: Ho-Lee Vol to Black Vol

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.