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When pricing a callable IRS (say only one call date) with a diffusion model (e.g. HW 1F) with a Montecarlo resolution, one can get the call probability on the call date versus maturing the date (which is the percentage of paths where the embedded swaption end up with a value > 0)

What would be an analytical way of implying a call probability using a closed-form of Black & Scholes (normal vol) when we only have one call date?

Thanks,

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The call probability is just the probability that the swap rate for the remaining life of the swap is below the strike rate. This is easily obtainable in a normal vol model, it is $$N((Strike-Forward Rate)/NormVol*Sqrt(T))$$ where T is time from now until call date, where $N$ is the cumulative Normal distribution.

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