Non-Negativity, Zero Lower Bound and Affine Interest Rate Models.

Summary This thesis presents several extensions to positive affine interest rate models. A first chapter introduces the concepts related to the models used in the following chapters. It details the definition of so-called affine processes, and the construction of asset price models obtained by non-arbitrage. Chapter 2 proposes a new estimation and filtering method for linear-quadratic state-space models. The next chapter applies this estimation method to the modeling of interbank spreads in the Eurozone, in order to decompose the fluctuations related to default and liquidity risk. Chapter 4 develops a new technique to create multivariate affine processes from their univariate counterparts, without imposing conditional independence between their components. The last chapter applies this method and derives a multivariate affine process in which some components can remain at zero for extended periods. Incorporated into an interest rate model, this process can efficiently account for zero-bottom rates.