Jean-Paul Renne

Default, liquidity and crises: an econometric framework

In this paper, we present a general discrete-time affine framework aimed at jointly modeling yield curves associated with different debtors. The underlying fixed-income securities may differ in terms of credit quality and/or in terms of liquidity. The risk factors follow conditionally Gaussian processes, with drifts and variance-covariance matrices that are subject to regime shifts described by a Markov chain with (historical) non-homogenous transition probabilities. While flexible, the model remains tractable. In particular, bond prices are given by quasi-explicit formulas. Various numerical examples are proposed, including a sector-contagion model and credit-rating modeling.

Fiscal Sustainability, Default Risk and Euro Area Sovereign Bond Spreads Markets

This paper develops an arbitrage-free affine term structure model of potentially defaultable sovereign bonds to model a cross-section of eight euro area government bond yield curves since January 1999. The existence of a common monetary policy under European Monetary Union determines the short end of the yield curves, whereas decentralized debt policies drive expected default probabilities and thereby spreads towards Germany, assumed to be free of default risk. The pricing factors are three observable area-wide macroeconomic variables and measures of national fiscal sustainability, which we proxy by expected changes in debt/GDP ratios of the respective countries. Our model explains spreads both before and during the crisis to an impressive extent. The deterioration in public finances was the major driver of the widening in spreads since 2008 through both heightened compensations for default risk and increases in risk premia. We also present perceived probabilities of sovereign default at any maturity and assess their elasticity to shifts in expected changes in debt/GDP ratios.

Credit and Liquidity Risks in Euro Area Sovereign Yield Curves

In this paper, we propose a model of the joint dynamics of euro-area sovereign yield curves. The arbitrage-free valuation framework involves five factors and two regimes, one of the latter being interpreted as a crisis regime. These common factors and regimes explain most of the fluctuations in euro-area yields and spreads. The regime-switching feature of the model turns out to be particularly relevant to capture the rise in volatility experienced by fixed-income markets over the last years. In our reduced-form set up, each country is characterized by a hazard rate, specified as some linear combinations of the factors and regimes. The hazard rates incorporate both liquidity and credit components, that we aim at disentangling. The estimation suggests that a substantial share of the changes in euro-area yield differentials is liquidity-driven. Our approach is consistent with the fact that sovereign default risk is not diversifiable, which gives rise to specific risk premia that are incorporated in spreads. Once liquidity-pricing effects and risk premia are filtered out of the spreads, we obtain estimates of the actual –or real-world– default probabilities. The latter turn out to be significantly lower than their risk-neutral counterparts.

Does uncertainty make a time-varying natural rate of interest irrelevant for the conduct of monetary policy?

We compute optimized monetary policy rules for the ECB when the euro area economy is described by a small empirical macroeconomic model with a time-varying natural interest rate which is positively correlated with fluctuations in trend output growth. We investigate the consequences of both measurement uncertainty with respect to unobservable variables and uncertainty about key model parameters. An optimized Taylor rule with time-varying neutral rate appears to perform well compared to the unconstrained optimal policy, and better than other simple rules found in the literature, even when it is penalized by taking into account both types of uncertainty.

Frequency-Domain Analysis of Debt Service in a Macro-Finance Model for the Euro Area

This paper illustrates how a parsimonious macro-finance model can be exploited to investigate the frequency-domain properties of debt service implied by various financing srategies. This orginal approach is valuable to public debt managers seeking to assess the fiscal-hedging properties of the financing strategies they implement. The model, inspired by Rudebusch and Wu (2008), is estimated on euro-area data over the period 1999-2009. At business-cycle frequencies, the variance of interest payments is lower when nominal long-term bonds are issued. From a budget-smoothing perspective, debt service variability plays a major role, but pro- or counter-cyclicality of debt service also matters. In this respect, the results suggest that while interest payments associated with medium- to long-term nominal bonds are negatively correlated with real activity, those associated with inflation-linked bonds and short-term nominal bonds tend to be pro-cyclical.

Fiscal Sustainability, Default Risk and Euro Area Sovereign Bond Spreads

This paper develops an arbitrage-free affine term structure model of potentially defaultable sovereign bonds to model a cross-section of eight euro area government bond yield curves since January 1999. The existence of a common monetary policy under European Monetary Union determines the short end of the yield curves, whereas decentralized debt policies drive expected default probabilities and thereby spreads towards Germany, assumed to be free of default risk. The pricing factors are three observable area-wide macroeconomic variables and measures of national fiscal sustainability, which we proxy by expected changes in debt/GDP ratios of the respective countries. Our model explains spreads both before and during the crisis to an impressive extent. The deterioration in public finances was the major driver of the widening in spreads since 2008 through both heightened compensations for default risk and increases in risk premia. We also present perceived probabilities of sovereign default at any maturity and assess their elasticity to shifts in expected changes in debt/GDP ratios.

Regime Switching and Bond Pricing

This article proposes an overview of the usefulness of the regime switching approach for building various kinds of bond pricing models and of the roles played by the regimes in these models. Both default-free and defaultable bonds are considered. The regimes can be used to capture stochastic drifts and/or volatilities, to represent discrete target rates, to incorporate business cycles or crises, to introduce contagion, to reproduce zero lower bound spells, or to evaluate the impact of standard or nonstandard monetary policies. From a technical point of view, we stress the key role of Markov chains, Compound Autoregressive (Car) processes, Regime Switching Car processes and multihorizon Laplace transforms.

A model of the euro-area yield curve with discrete policy rates

This paper presents a no-arbitrage yield-curve model that explicitly incorporates the central-bank policy rate. This model is consistent with the existence of a lower bound for nominal interest rates, which makes it particularly relevant in the current context of extremely low interest rates. Changes in the policy rates depend on the monetary-policy phase, that can be either in an easing, status quo or tightening mode. The estimation of the model, based on daily euro-area yield data, reveals the strong influence of the monetary-policy phases on the shape of the yield curve. This relationship can, in turn, be exploited to estimate the probabilities of being in the different monetary-policy phases. The model is also used to compute term premiums, that are the parts of the yields reflecting the aversion of investors to interest rate risk. The results point to the existence of statistically significant premiums for many dates, even for short horizons.

Credit and Liquidity in Interbank Rates: A Quadratic Approach

A bank that lends on the unsecured market requires compensations for facing the default risk of the borrowing bank (credit risk) and the risk associated to its own future funding needs (liquidity risk). In this paper, we propose a quadratic term-structure model of the spreads between unsecured and risk-free interbank rates. Our no-arbitrage econometric framework allows us to decompose the term structure of spreads into credit and liquidity components and to identify risk premia associated with each of these two risks. Our results suggest that, over the period 2012–2013, most of the reduction in interbank spreads comes from a decrease in liquidity-related risk components.

A Quadratic Kalman Filter

We propose a new filtering and smoothing technique for non-linear state-space models. Observed variables are quadratic functions of latent factors following a Gaussian VAR. Stacking the vector of factors with its vectorized outer-product, we form an augmented state vector whose first two conditional moments are known in closed-form. We also provide analytical formulae for the unconditional moments of this augmented vector. Our new quadratic Kalman filter (Qkf) exploits these properties to formulate fast and simple filtering and smoothing algorithms. A first simulation study emphasizes that the Qkf outperforms the extended and unscented approaches in the filtering exercise showing up to 70% RMSEs improvement of filtered values. Second, we provide evidence that Qkf-based maximum-likelihood estimates of model parameters always possess lower bias or lower RMSEs that the alternative estimators.