Solvable Affine Processes on the Euclidean State Space

Abstract

Chapter 9 continues the discussion of affine processes from Chaps. 7 and 8, but we now pursue a different approach, namely the approach of Grasselli and Tebaldi. In Chap. 7, we demonstrate that the defining property of affine processes, namely that their characteristic function is exponentially affine in the state variables, gives us an important starting point when deriving a formula for this characteristic function. This approach though does not provide us with a recipe of how to arrive at the final result and it also does not guarantee that an explicit formula is in fact available. The Grasselli-Tebaldi approach addresses precisely both of these problems: in a first step, we identify those affine processes for which we can obtain a closed-form solution for the characteristic function, and in a second step we provide an algorithm for how to obtain this explicit formula. We then proceed to demonstrate the approach using examples, which include for example the Heston model, but also a multifactor version thereof. It is again envisaged that this chapter and the detailed discussion of the examples provided encourages readers to apply this approach to their fields of interest.