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The LIBOR Market Model (LMM) is the first model of interest rates dynamics consistent
with the market practice of pricing interest rate derivatives. The model was created in 1994 by
Kristian Miltersen, Klaus Sandmann and Dieter Sondermann (1997), then developed in 1995
to a form applicable in practice by Alan Brace, Dariusz Gatarek and Marek Musiela (1997).
Its current form (including the name) belongs to Farshid Jamshidian (1997) and is based an
abstract formulation of LMM by Marek Musiela and Marek Rutkowski (1997a). The LMM
is also called Brace-Gatarek-Musiela (BGM) model. Some authors claim that the model
was discovered independently, that is not true – there was close collaboration between the
Bonn group (Miltersen, Sandmann and Sondermann), the Sydney group (Brace, Gatarek and
Musiela), Marek Rutkowski in Warsaw and Farshid Jamshidian in London. Its popularity
is a result of consistency with practice, allowing the pricing of vanilla products in LMM
to be reduced to using standard market formulae. However ease of use does not suffice to
win the market, and there are numerous theoretical advantages to the LMM as well. The
LMM was preceded by so called short rate models – where the dynamics of all interest rates
was determined by the dynamics of the overnight rate. This is a counterintuitive property
but practitioners learned how to apply it to a relatively high degree of effectiveness. The
next stage was the seminal Heath-Jarrow-Morton (HJM) model (1992), where attention was
shifted correctly from the artificial notion of the short rate to the whole term structure
of interest rates – a mathematically interesting problem of random dynamics in infinite
dimension. We may say that all questions were already answered, the main contribution
of the LMM is one more shift of attention to instantaneous forward rates and, interesting
for theorists, to forward rates with market compounding – quarterly, semi-annual, annual,
etc. The history of science has told us that the simple and obvious properties are the most
difficult to spot.
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