Affine Diffusion Processes on the Euclidean Space

Abstract

In this chapter, we discuss affine process, a class of processes that has recently received much attention in the literature. Recalling that the underlying theme of this book is the explicit computation of functionals of multidimensional diffusions, we realize quickly that affine diffusions tie in naturally with this theme: the defining property of an affine process is that its characteristic function is exponentially affine in the state variables, a crucial starting point when deriving explicit formulas for the characteristic function. In a first part of the chapter, we discuss the theory of affine processes. Subsequently, we recall how affine processes have been applied under the classical risk neutral paradigm. Finally, we show how affine processes can be employed under the benchmark approach introduced in Chap. 1. We demonstrate how so-called “benchmarked Laplace transforms” arise naturally in this context and also how to introduce forward measures under the benchmark approach. In both cases, the transforms presented in Chap. 5 turn out to be very useful.