BFS 2002

Contributed Talk

Endogenous interest rate dynamics in asset markets

John Schoenmakers, Oliver Reiß, Martin Schweizer

Starting from a general Ito process model with more assets than driving Brownian motions, we study the term structure model endogenously induced by this complete market. In the Markovian diffusion case, we provide the resulting HJM description and point out a link to finite factor models. But the main contribution is the conceptual approach of considering assets and interest rates within one model which is completely specified by the dynamics of the assets alone. This allows endogenous derivations of dynamic relations between assets and interest rates from global structural assumptions (homogeneity and some spherical symmetry) on the market. In particular, we obtain connections between the short rate, risk premia, the numeraire portfolio (the inverse of the pricing kernel in fact) and certain observable indices. The presented work is related to studies of Fisher & Gilles (2000), Kazemi (1992) and E. Platen (1999, 2000).