# How popular is the Linear Gauss Markov (LGM) model?

Some friends recommend to me Linear Gauss Markov model, saying it's interesting to have a look at it. Basically it's a framework different from HJM, with potential to extend, and the merit is that it's linear, so won't be so interwined as Hull White models, -- or so I was told.

I just did a brief search, it's from Patrick Hagan, there are several of his papers,

• "Markov Interest Rate Models", 1999, about the model, and
• "Methodology for Callable Swaps and Bermudan Exercise Into Swaptions", 2004
• "Accrual Swaps and Rangge Notes", 2005, about the calibration

But besides that seems LGM was not so popular in other sources. For example, Damiano Brigo's book "Interest Rate Models Theory and Practice" and Leif Andersen's "Interest Rate Modeling" are two famous books, but neither mentioned LGM model.

Did I miss something, or it's not so popular because for some reason, or did the two books just happen not to contain LGM?

In Andersen & Piterbarg's book, LGM is referred to as "The Hagan and Woodward Parameterization" and treated separately in 11.3.2.6.

The fact that this practice-oriented book devotes a couple of pages would imply LGM is of practical use in the real market. I know two large software providers adopt LGM.

• I haven't read that yet ... But sounds Andersen thinks the merits of LGM is parameterization? Would you pls say a bit more on that? – athos Aug 12 '14 at 14:09
• Since it's from Hagan, I suppose one is Bloomberg :p – athos Aug 12 '14 at 14:59

It's a refashioning of the full Hull-White extension of the Vasicek Model. It's explored at length in Modern Derivatives Pricing and Credit Exposure Analyis, wherein the equivalency is shown. The advantages of the reformulation are that semi-analytic results are more readily available, and that it is only necessary to keep track of one Wiener process during simulations (rather than 2 due to the $$\int dW$$ term in HW).