Basically, short rate dynamics yield the following expression:
or, more generally:
Depending on whether wt is a single Brownian or a vector, the model is said to be one-factor or multi-factor. Also, the diffusion process can involve several correlated variables (e.g., the Gaussian additive model).
In the literature, it is common to read that models are classified into to two main categories:
In this section, we will address successively one-factor, two-factor, and forward curve models, without reference to any other criterion. Obviously, one chapter cannot cover the matter exhaustively, but the models presented give a global overview of the main features of interest rate modeling theory: further on, these models will be used for pricing some interest rate exotics.
The role of the forward measure By definition, under the forward measure Qt, any asset denominated in zero-bonds has the following martingale property:
On the other hand, under ...