# Call Probability of European callable IRS

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,

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.