We consider a set of Markovian processes with Stochastic transition matrices. This specification extends the standard stochastic intensity model introduced by Cox in the two state case. Such a model is appropriate for the joint analysis of rating histories of several corporates, including the...

In this paper we consider an incomplete market framework and explain how to use jointly observed prices of the underlying asset and some derivatives written on this asset for an efficient pricing of other derivatives. This question involves two types of moment restrictions, which can be written...

In this article we explain how to use rating histories provided by the internal scoring systems of banks and rating agencies in order to predict the future risk of a set of borrowers. The method is developed following the steps suggested by the Basle Committee. To introduce both migration...

The aim of this paper is to extend the results of Jarrow, Yu (2001) on the spread term structures of corporate bonds. We first consider different characterisations of these term structures, when the available information corresponds to the default histories of the firms. The approach is then...

The aim of this paper is to explain why cross-sectional estimated migration correlations displayed in the academic and professional literature can be either not consistent, or inefficient, and to discuss alternative approaches. The analysis relies on a model with stochastic migration in which...

This paper extends to the multiasset framework the closed-form solution for options with stochastic volatility derived in Heston (1993) and Ball and Roma (1994). This extension introduces a risk premium in the return equation and considers Wishart dynamics for the process of the stochastic...

In one of the early attempts to model stochastic volatility, Clark [1973] conjectured that the size of asset price movements is tied to the rate at which transactions occur. To formally analyze the econometric implications, he distinguished between transaction time and calendar time. The present...

Subordinated stochastic processes, also called time deformed stochastic processes, have been proposed in a variety of contexts to describe asset price behavior. They are used when the movement of prices is tied to the number of market transactions, trading volume or the more elusive concept of...

This paper introduces impulse response analysis for nonlinear processes based on the concept of nonlinear innovation. Our approach borrows from the traditional linear impulse response analysis in that we consider shocks to innovations of a process. It also extends the methods of nonlinear...

Continuous-time affine models have been recently introduced in the theoretical financial literature on credit risk. They provide a coherent modeling, rather easy to implement, but have not yet encountered the expected success among practitioners and regulators. This is likely due to a lack of...