callable bonds with FDM

I am thinking of implementing a model to price callable bonds on a finite difference grid. I wonder how the Price to worst yield model will relate to it in terms of risks(or should do). What I expect is that with a simple yield to workout date there is only one single "best" call time which I can find by computing the min yield(often it is the first call date). And my model will yield a distribution of call dates but the mean of that should coincide with the workout date and as a result all risks are about the same?

How does it work when the best workout date is the first call date though? My model's distribution can have its mode on the first call date but not the mean and as a result don't I have larger risks with a stochastic model as duration would be larger in the model case?

• I do not see why the mean should coincide with the workout date, why do you think that is the case? Jul 21, 2021 at 8:39
• @TrevorHansen it actually doesn't it. After some testing and thinking I can see it doesn't. Whenever you use stochastic model the Workout date is the average and always is pushed further, this is not the first call date ever, while price to yield can return the first call date. In such cases the models yield very different duration and as a result different risk. I wonder how I would deal with these numbers then, obviously the larger risk is not favorable. Jul 21, 2021 at 13:18
• I think the numbers you are getting are fine. The difference between the workout date and the mean will be your option premium. In your example of first call date, even in the case when the workout date is expected to be the first call date based on current market environment, there is a probability that the bond will not be called (due to change in rates for example). The risk related to the bond not being called will be the difference between the duration to first call and duration to mean. This is analogous to an option that is out of the money, but still has a non-zero market value. Jul 22, 2021 at 7:17
• This is the reason that bonds with large callable features often trade at a premium to the non-callable counterparts under the current market conditions. Jul 22, 2021 at 7:18
• @TrevorHansen how do trading desks handle it, as their risks under stochastic modeling is growing so large that they trigger VAR limits? would I need to make some adjustment to the price in order to construct the model that provides me more consistent risk between price to yield and a stochastic model? Jul 22, 2021 at 15:07