A Multifactor Model of Credit Spreads

Abstract

We represent credit spreads across ratings as a function of common unobservable factors of the meanreverting normal (Vasicek) form. Using a state-space approach we estimate the factors, their process parameters, and the exposure of each observed credit spread series to each factor. We find that most of the systematic variation across credit spreads is captured by three factors. The factors are closely related to the implied volatility index (VIX), the long bond rate, and S&P500 returns, supporting the predictions of structural models of default at an aggregate level. By making no prior assumption about the determinants of yield spread dynamics, our study provides an original and independent test of theory. The results also contribute to the current debate about the role of liquidity in corporate yield spreads. While recent empirical literature shows that the level and time-variation in corporate yield spreads is driven primarily by a systematic liquidity risk factor, we find that the three most important drivers of yield spread levels relate to macroeconomic variables. This suggests that liquidity risk is largely driven by the same factors as default risk.

Credit Risk and Incomplete Information: Filtering and Em Parameter Estimation

“…In many studies dealing with term structure modeling n is taken as n = 3 (see Baadsgaard et al (2000), Chen & Scott (2003)) while more recent empirical studies from the credit risk literature suggest n = 3 (Bhar & Handzic (2008)), n = 4 (Jacobs & Li (2008)), or n = 6 (Feldhütter & Lando (2008)). The values of the factors are described by an n-dimensional process Ψ t that is (F t )-adapted and that we assume satisfies the following dynamics…”

“…Besides enhancing the model flexibility, latent factors can indeed have a meaningful economic interpretation as documented e.g. in Das et al (2007), Duffie et al (2009) and Bhar & Handzic (2008) where, on the basis of empirical evidence, it is shown that unobservable stochastic factor processes driving the default intensities are needed on top of observable covariates in order to explain clustering of defaults in historical data and large comovements of credit spreads. In addition, the formulation of a model under incomplete information has the advantage of avoiding a possibly inadequate specification of the factor model.…”

“…This fact is one of the major advantages of our methodology over the existing literature that deals with partially observed state-observation models where parameter estimation is typically done by maximizing the likelihood of the innovations obtained from the Extended Kalman Filter (EKF). Relevant contributions in this latter sense include Baadsgaard et al (2000), Chen & Scott (2003), Duan & Simonato (1999), Geyer & Pichler (1999), Lund (1997) in the context of term structure models and, more recently, Bhar & Handzic (2008), Jacobs & Li (2008), Feldhütter & Lando (2008 in the context of credit risk. In addition, our results extend those of Elliott & Krishnamurthy (1999) and Elliott & Hyndman (2006) to models driven by a multivariate stochastic factor process with nonlinear dynamics.…”

Mathematical and Statistical Methods for Actuarial Sciences and Finance

“…Observable macroeconomic covariates that may characterize the general state of the economy, as well as sectorial, geographic and idiosyncratic components can also be included. Indeed, such variables have been shown to play a significant role in explaining the level of credit risk (see [4,11,17,18]). Such a modeling approach can be seen as a dynamic generalization of the so-called frailty-based approach, which also allows one to introduce information-driven default contagion effects (see [2,11,23]).…”

“…Due to(3), this also implies that the risk premium is unobservable, as in[3] and[22] 4. This setting can also be extended to include the whole rating transition matrix among the observations if we assume that the intensities driving the rating transitions are of the form(2).…”