On the interface of probabilistic and PDE methods in a multifactor term structure theory

Abstract

Within the general framework of a multifactor term structure model, the fundamental partial differential equation (PDE) satisfied by a default-free zero-coupon bond price is derived via a martingale-oriented approach. Using this PDE, a result characterizing a model belonging to an exponential affine class is established using only a system of partial derivatives. It is also shown that the solution to the bond price PDE has the conditional expectation representation arising in martingale pricing through the application of a multi-dimensional version of Itô's lemma and a property of the stochastic integral.

Acknowledgments

The author wishes to acknowledge the hospitality of the Department of Applied Mathematics, University of Adelaide, Australia, where part of this manuscript was written; and to thank the Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, USA where this work was completed.