Linear Gauss–Markov Models and Their Hull–White Connection
Summary
The document discusses the practical standing of the Linear Gauss–Markov model for interest rates and its relationship to other short-rate frameworks. It reports that one reference treats LGM under the name “Hagan and Woodward Parameterization,” and that two large software providers use it. Another answer characterizes LGM as a reformulation of the full Hull–White extension of the Vasicek model.
The stated advantages are that the reformulation makes semi-analytic results more accessible and requires tracking one Wiener process in simulations, instead of two in the described Hull–White setup. These points offer reasons the framework may be useful despite limited coverage in some commonly cited books. The evidence in the document is anecdotal: it cites brief textbook treatment and software adoption but gives no adoption figures, model comparison, calibration results, or pricing tests. It does not establish that LGM is universally preferred or superior.
Key ideas
- LGM is described as a reparameterization of the full Hull–White extension of the Vasicek model.
- One rates text discusses LGM under the Hagan–Woodward parameterization name.
- The document reports adoption by two large software providers as evidence of practical use.
- The reformulation is said to make semi-analytic results more accessible.
- The described simulations require tracking one Wiener process rather than two.
Tags
Full text
# How popular is the Linear Gauss Markov (LGM) model? # 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? ## Answer by a japanese (score 3, accepted) https://quant.stackexchange.com/a/14372 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. ## Answer by lampishthing (score 2) https://quant.stackexchange.com/a/43519 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).
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.