DYNAMIC QUANTILE MODELS

This paper introduces new dynamic quantile models called the Dynamic Additive Quantile (DAQ) model and Quantile Factor Model (QFM) for univariate time series and panel data, respectively. The Dynamic Additive Quantile (DAQ) model is suitable for applications to financial data such as univariate returns, and can be used for computation and updating of the Value-at-Risk. The Quantile Factor Mode (QFM) is a multivariate model that can represent the dynamics of cross-sectional distributions of returns, individual incomes, and corporate ratings. The estimation method proposed in the paper relies on an optimization criterion based on the inverse KLIC measure. Goodness of fit tests and diagnostic tools for fit assessment are also provided. For illustration, the models are estimated on stock return data form the Toronto Stock Exchange (TSX).Value-at-Risk, Factor Model, Information Criterion, Income Inequality, Panel Data, Loss-Given-Default

A term structure model with level factor cannot be realistic and arbitrage free

A large part of the term structure literature interprets the first underlying factors as a level factor, a slope factor, and a curvature factor. In this paper we consider factor models interpretable as a level factor model, a level and a slope factor model, respectively. We prove that such models are compatible with no-arbitrage restrictions and the positivity of rates either under rather unrealistic conditions on the dynamic of the short term interest rate, or at the cost of explosive long-term interest rates. This introduces some doubt on the relevance of the level and slope interpretations of factors in term structure models.Interest Rate, Term Structure, Affine Model, No Arbitrage, Level Factor, Slope Factor.

The Ordered Qualitative Model For Credit Rating Transitions

Information on the expected changes in credit quality of obligors is contained in credit migration matrices which trace out the movements of firms across ratings categories in a given period of time and in a given group of bond issuers. The rating matrices provided by Moody’s, Standard &Poor’s and Fitch became crucial inputs to many applications, including the assessment of risk on corporate credit portfolios (CreditVar) and credit derivatives pricing. We propose a factor probit model for modeling and prediction of credit rating matrices that are assumed to be stochastic and driven by a latent factor. The filtered latent factor path reveals the effect of the economic cycle on corporate credit ratings, and provides evidence in support of the PIT (point-in-time) rating philosophy. The factor probit model also yields the estimates of cross-sectional correlations in rating transitions that are documented empirically but not fully accounted for in the literature and in the regulatory rules established by the Basle Committee.Credit Rating, Migration, Migration Correlation, Credit Risk, Probit Model, Latent Factor, Business Cycle.

Coherency Conditions In Simultaneous Linear Equation Models With Endogenous Switching Regimes

In modeling disequilibrium macroeconomic systems which one would want to subject to econometric estimation one typically faces the problem of whether the structural model can determine a unique equilibrium. The problem inherits a special form because the regimes in which the equilibria can lie are each linear. By placing restrictions on the parameters that insure the uniqueness of such a solution for each value of the exogenous and random variables, we can improve the estimation procedure. This paper provides necessary and sufficient conditions for uniqueness -- or "coherency." These conditions are applied to a variety of models that have been prominent in the literature on econometrics with 'switching regimes' such as those of self-selectivity (Maddala), simultaneous equation tobit and probit (Amemiya, Schmidt) and multi-market macroeconomic disequilibrium (Gourieroux, Laffont and Nonfort).

Sensitivity Analysis of Values at Risk

The aim of this paper is to analyze the sensitivity of Value at Risk (VaR) with respect to portfolio allocation. We derive analytical expressions for the first and second derivatives of the Value at Risk, and explain how they can be used to simplify statistical inference and to perform a local analysis of the Value at Risk. An empirical illustration of such an analysis is given for a portfolio of French stocks.

The Wishart short rate model

We consider a short rate model, driven by a stochastic process on the cone of positive semidefinite matrices. We derive sufficient conditions ensuring that the model replicates normal, inverse or humped yield curves

Structural Modelling of Dynamic Networks and Identifying Maximum Likelihood

This paper considers nonlinear dynamic models where the main parameter of interest is a nonnegative matrix characterizing the network (contagion) effects. This network matrix is usually constrained either by assuming a limited number of nonzero elements (sparsity), or by considering a reduced rank approach for nonnegative matrix factorization (NMF). We follow the latter approach and develop a new probabilistic NMF method. We introduce a new Identifying Maximum Likelihood (IML) method for consistent estimation of the identified set of admissible NMF's and derive its asymptotic distribution. Moreover, we propose a maximum likelihood estimator of the parameter matrix for a given non-negative rank, derive its asymptotic distribution and the associated efficiency bound