I try to implement the Libor Market Model in a negative interest environment. As the LMM is a model which assumes a lognormal distribution of forward rates, in its basic form, it cannot deal with this setting. I know that there is a normal (Bachelier) version of the LMM, but I cannot find details about it and its implementation. Right now I use the following formula under the forward measure for the dynamik of the forward rates: enter image description here enter image description here

How do I have to adjust this, when I want to use the normal LMM?

  • $\begingroup$ If you look in the literature for Generalized Vasicek models, they are gaussian rather than exponentiated gaussian. Like LMM they match the market "exactly". Note that formulations I have seen in the literature are all in continuous time so you have to translate a little. $\endgroup$
    – Brian B
    Mar 1 at 17:35


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