We present some properties concerning heterogeneity using as illustrations duration data models. We first study the links between aggregate and disaggregate concepts. This allows to give some precise definitions of the heterogeneity biases and of the mover stayer phenomenon. We also introduce...

The aim of this paper is the determination of the term structure of interest rates from observations of the prices of fixed-income bonds. We first introduce factor models to describe the evolution of prices of zero-coupon bonds, and we derive the constraints induced by the arbitrage free...

The exponential affine pricing principle is applied to the family of skewed Laplace historical distributions. The risk-neutral distribution is shown to belong to the same family and a closed form pricing formula for a European call is derived. This formula is a direct competitor of the...

One major topic in empirical studies on Finance is the correlation of default risk. Correlation is a main driver for credit risk on a credit portfolio and for bank's capital requirement under the Basel II Accord. However, empirical evidence on the magnitude of correlation is rather scarce,...

A number of interesting properties of stationary processes, in particular Wold decomposition, can be derived using a geometrical approach. In this paper we introduce the notions of recent past and old past by means of well chosen vector spaces. A geometrical study of these spaces and of their...

In this paper we discuss the usefulness, for models with heterogeneity, of simulation techniques in inference procedures, like maximum likelihood method, generalized moments method or pseudo maximum likelihood methods. These procedures are studied from the point of view of consistency,...

We introduce an ordering on the scoring functions used in credit and insurance problems; this ordering corresponds to the idea of a more precise selection of the customers. It is naturally based on the comparison of some curves, called performance, selection and discrimination curves. Various...

This paper introduces a concept of innovation for the analysis of nonlinear dynamics. We show that nonlinear processes can be represented as functions of current and lagged values of such innovations. The residuals from nonlinear dynamic models axe used to construct various specification tests....