# Call probability of a callable swap

For one call date,

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−ForwardRate)/NormVol∗Sqrt(T)) where T is time from now until call date, where N is the cumulative Normal distribution.

I just want to know How can we apply this formula when we have multiple callable dates? For exemple each year on a 10Y maturity.

Thanks,

• For a Bermudan call schedule, in general, you usually need a Monte Carlo simulation for most calculations. Oct 20, 2022 at 12:47
• Agreed- the given formula cannot be used to calculate the call probability in a Bermudan option
– dm63
Oct 21, 2022 at 11:00
• that's not for a bermudan option. Here, there is callable dates (1 per year for example), you can't execute when you want as a bermudan option. Oct 21, 2022 at 15:01
• Hi Lrzo48, well that's exactly the definition of Bermudan exercise; it's multiple discrete call or put dates. I think you're confusing it with an American option. That said, for both the simple formula you provided is not sufficient, as it relies on a single expiry date (European style option). Oct 21, 2022 at 15:14
• Say we have a discrete case where the underlier (say a stock) can only take on integer values (prices). For stock at the value $s$ you move to price $t$ with probability $P_s(t)$. If all that is known, then you can in principle answer any question about probability of exceeding the strike at any of the steps in time, or combinations thereof (no?), using Bayes and all that. So why would simulation be needed -- i.e. you can a tedious calculation instead? Assuming moving to continuous case is OK, but I'm no expert. Oct 22, 2022 at 21:54