Stabsseminar med Mark Davis

Mark Davis fra Imperial College holder stabsseminar ved Institutt for foretak fredag.

15.01.2003 - Anette W. Petersen

Tema: Finite-dimensional Models of the Yield Curve

Tid: Fredag 17. januar, kl. 12.15-14.30

Sted: Karl Borch's aud.

Abstract:
Models of the HJM family generally represent the yield curve as the solution of a stochastic differential equation evolving in an infinite-dimensional space. It is an important question to determine under what conditions the solution is actually finite-dimensional, i.e. the yield curve at any time can be expressed as a point function of some finite-dimensional state vector process. Several authors have discovered special volatility structures under which this is the case, while others have investigated general geometric conditions. This paper takes a different point of view. In reality, the yield curve is intrinsically finitedimensional in that it is constructed from a finite set of market data: short-term interest rates, interest rate futures and swap rates. We ask whether it is possible, given a stochastic differential equation model for the market rates, to construct consistent and arbitrage-free prices for zero-coupon bonds of arbitrary maturities. We demonstrate that this can be done in some simple cases, but that naive algorithms such as those used in conventional 'yield curve generators' can easily create arbitrage opportunities.

Kontaktperson: Hans K. Hvide (59283).