July 26th, 2023, 6:31 pm
Thanks. And yes, the example in the note is simplified, in reality I use e.g. sigma = 0.0030 and kappa = 0.50 for one of the factors, but the instability remains.
In the meantime I think the issue is quite obvious. When you develop the multi factor Hull-White model from the HJM equation you naturally arrive at a point where you are tempted to use the state from the LGM formulation because of its simple SDE. But then you _want_ to switch to a mean reverting state exactly because of the issue described above. The Piterbarg / Andersen book is quite explicit on this, see Proposition 12.1.1, Equation (12.3) and the remark at the beginning of section 12.1.1.1.