COLLOQUIUM
3:00 p.m., Friday (October 5)
Math Annex 1100
Tomas Björk
Stockholm School of Economics
On the geometry of interest rate models
Abstract: The purpose of this talk is to give an overview of some recent work
concerning the structural and geometric properties of the evolution
of the forward rate curve in an arbitrage free bond market. The main
problems to be discussed are as follows.
1. When is a given forward rate model consistent with a given family
of forward rate curves?
2. When can the inherently infinite dimensional forward rate process
be realized by means of a finite dimensional state space model?
We consider interest rate models of HeathJarrowMorton type, where
the forward rates
are driven by a multidimensional Wiener process, and where the
volatility is allowed to be an arbitrary smooth
functional of the present forward rate curve. Within this framework we
give necessary and sufficient conditions for consistency, as well as
for
the existence of a finite dimensional realization, in terms of the
forward rate volatilities.
We also study stochastic volatility HJM models, and we provide a
systematic method for the construction of concrete realizations.
Refreshments will be served at 2:45 p.m. (Math Lounge, MATX 1115).
