Interest Rates

Abstract

We are going to use a single-factor interest rate model, the Linear Gauss Markov model (LGM) which has been propagated by Patrick Hagan [77], see also Hagan and Woodward’s 1999 paper [81] and Andersen’s and Piterbarg’s summary of the model in [8]. The LGM model is closely related to the one-factor Hull-White model with time-dependent parameters. It is formulated in an unusual measure (none of the bank account, forward or annuity measures we have seen before). This makes it particularly tractable, as we will show for a few examples below. A step-by-step derivation of the LGM model from the one-factor Hull-White model is provided in Appendix E.