Chapter 2: FAQs 183
What is the LIBOR Market Model and
Its Principal Applications in Finance?
Short Answer
The LIBOR Market Model (LMM), also known as the
BGM or BGM/J model, is a model for the stochastic
evolution of forward interest rates. Its main strength
over other interest rate models is that it describes the
evolution of forward rates that exist, at market-traded
maturities, as opposed to theoretical constructs such as
the spot interest rate.
Example
In the LMM the variables are a set of forward rates
for traded, simple fixed-income instruments. The para-
meters are volatilities of these and correlations between
them. From no arbitrage we can find the risk-neutral
drift rates for these variables. The model is then used
to price other instruments.
Long Answer
The history of interest-rate modelling begins with deter-
ministic rates, and the ideas of yield to maturity, dur-
ation, etc. The assumption of determinism is not at all
satisfactory for pricing derivatives however, because of
Jensen’s Inequality.
In 1976 Fischer Black introduced the idea of treat-
ing bonds as underlying assets so as to use the
Black–Scholes equity option formulæ for fixed-income
instruments. This is also not entirely satisfactory since
there can be contradictions in this approach. On one
hand bond prices are random, yet on the other hand
interest rates used for discounting from expiration to
the present are deterministic. An internally consistent
stochastic rates approach was needed.
