First volatility guess

The idea is to freeze all stochastic bonds to find the best possible solution.

And then apply solver to find the real solution (with stochastic bonds).

Hull White swap rate variance

Any model is just a dynamic.

Hull White models short rate which is the basic block of all IRD products.

By definition of swap rate:

where we are entering to the Hull white world by assuming Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator.

Thus swap rate now is a function of pure Ornstein-Uhlenbeck Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator. process with some deterministic coefficients. Skipping them we can roughly represent swap rate as:

Thus using Itô we can derive SDE for Unknown macro: formula. Click on this message for details.
The [formula] macro is not in the list of registered macros. Verify the spelling or contact your administrator. and then compute its variance.