200 Frequently Asked Questions In Quantitative Finance
traded prices. Now the prices may be correct based on
the statistics of the past but are they correct going for-
ward? The models of Ho & Lee and Hull & White are a
cross between the equilibrium models and no-arbitrage
models. Superficially they look very similar to the for-
mer but by making one or more of the parameters time
dependent they can be calibrated to market prices and
so supposedly remove arbitrage opportunities. But still,
if the parameters, be they constant or functions, are
not stable then we will have arbitrage. But the question
is whether that arbitrage is foreseeable. The interest
rate models of HJM and BGM match market prices each
day and are therefore even more in the no-arbitrage
camp.
References and Further Reading
Brace, A, Gatarek, D & Musiela, M 1997 The market model of
interest rate dynamics.Mathematical Finance 7 127–154
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
Hull, JC & White, A 1990 Pricing interest rate derivative secu-
rities.Review of Financial Studies 3 573–592
Vasicek, OA 1977 An equilibrium characterization of the term
structure.Journal of Financial Economics 5 177–188
