186 Frequently Asked Questions In Quantitative Finance
Again, the LMM is solved by simulation with the yield
curve ‘today’ being the initial data. Calibration to the
yield curve is therefore automatic. The LMM can also
be made to be consistent with the standard approach
for pricing caps, floors and swaptions using Black 1976.
Thus calibration to volatility- and correlation-dependent
liquid instruments can also be achieved.
Such a wide variety of interest models have been
suggested because there has not been a universally
accepted model. This is in contrast to the equity world
in which the lognormal random walk is a starting point
for almost all models. Whether the LMM is a good model
in terms of scientific accuracy is another matter, but
its ease of use and calibration and its relationship with
standard models make it very appealing to practitioners.
References and Further Reading
Brace, A, Gatarek, D & Musiela, M 1997 The market model of
interest rate dynamics.Mathematical Finance 7 127–154
Brennan, M & Schwartz, E 1982 An equilibrium model of bond
pricing and a test of market efficiency.Journal of Financial
and Quantitative Analysis 17 301–329
Cox, J, Ingersoll, J & Ross, S 1985 A theory of the term struc-
ture of interest rates.Econometrica 53 385–467
Fong, G & Vasicek, O 1991, Interest rate volatility as a stochas-
tic factor. Working Paper
Heath, D, Jarrow, R & Morton, A 1992 Bond pricing and the
term structure of interest rates: a new methodology.Econo-
metrica 60 77–105
Ho, T & Lee, S 1986 Term structure movements and pric-
ing interest rate contingent claims.Journal of Finance 42
1129–1142
