In this part of the book we apply the model intuition hopefully built with the treatment in Parts I and II and the solid understanding of the conditions of noarbitrage developed in Part III in order to solve a variety of affine models. By ‘solving’, we mean finding expressions for bond prices, yields, volatilities, etc, as a function of the parameters of the mean-reverting processes followed by the state variables, and of their initial values.

First we look at the Vasicek model (Chapter 16), and then, in Chapters 17 and 18, we generalize the formalism to the case of several variables.

With the generalizations presented in Chapters 17 and 18, we fulfill two purposes: first, we give the reader the tools to handle virtually any affine model that she may encounter – or, indeed, that she may wish to build herself; second, we introduce the reader to the language needed to read the modern literature on the topic – where, just to be clear, ‘modern literature’ means the literature written in the last twenty years or so, not in the last six months.

I will not provide the most general solution to the Partial Differential Equations that we shall obtain, but, as usual, I will trade at a very high exchange rate generality for simplicity.