I would like to know how the FDM models gets adapted when bonds have very long maturity, e.g. 150Y. There are a number of fixed-to-float perpetuals on the market that I would like to be able to value.

One valuation approach is to consider the price to yield formula and compute the lowest yield. That will produce a workout date for which I can compute all the risks. Very often it is the first call date and essentially shortest duration possible.

Another approach is to assume some stochastic model for the yield. But that allows every exercise date to have a possibility of a call and as a result, even call dates that are 150Y away do have a chance of a call as on the FDM grid I have a range of values and for some nodes I am in the money. As a result, the workout date doesn't have to coincide with the workout date of the price to yield and can make a big impact on the risk. Even though the first date is the mode for the distribution for call dates, it is not one single call date.

I wonder if there is a special way of handling those fixed-to-float perpetuals when pricing with finite differences so the risk is more consistent? I see big risk numbers differences and I think this is due to the very different nature of the models where the latter assumes the distribution for callability and price to yield returns one fixed value.