Modeling the Dynamics of Credit Spreads with Stochastic Volatility

The paper investigates a two-factor affine model for the credit spreads on corporate bonds. The first factor can be interpreted as the level of the spread, and the second factor is the volatility of the spread. The riskless interest rate is modeled using a standard two-factor affine model, thus leading to a four-factor model for corporate yields. This approach allows us to model the volatility of corporate credit spreads as stochastic, and also allows us to capture higher moments of credit spreads. We use an extended Kalman filter approach to estimate our model on corporate bond prices for 108 firms. The model is found to be successful at fitting actual corporate bond credit spreads, resulting in a significantly lower root mean square error than a standard alternative model in both in-sample and out-of-sample analyses. In addition, key properties of actual credit spreads are better captured by the model. Dans cet article, nous modélisons l'écart de crédit sur obligations d'entreprise avec un modèle affin à deux facteurs. Le premier facteur s'interprète comme le niveau de l'écart et le deuxième comme sa volatilité. Le taux d'intérêt sans risque est modélisé selon un modèle affin à deux facteurs standard, ce qui conduit à un modèle à quatre facteurs pour les rendements d'obligations d'entreprise. Cette approche nous permet de modéliser la volatilité des écarts de crédit de manière stochastique et également de capter des moments des écarts de crédit d'ordres plus élevés. Nous utilisons une approche de filtre de Kalman étendu pour estimer notre modèle à partir des prix des obligations de 108 entreprises. Le modèle s'avère performant dans sa reproduction des écarts de crédit empiriques des obligations d'entreprise et mène à une racine des erreurs moyennes quadratiques significativement plus petite que celle d'un modèle alternatif standard, et ce aussi bien dans l'échantillon que lors d'analyses hors échantillon. De plus, le modèle capte également mieux certaines caractéristiques empiriques importantes des écarts de crédit sur obligations d'entreprise.credit risk, credit spreads, reduced form models, stochastic volatility, risque de crédit; écarts de crédit; modèles à forme réduite; volatilité stochastique

Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model

We present a two-factor stochastic default intensity and interest rate model for pricing single-name default swaptions. The specific positive square root processes considered fall in the relatively tractable class of affine jump diffusions while allowing for inclusion of stochastic volatility and jumps in default swap spreads. The parameters of the short rate dynamics are first calibrated to the interest rates markets, before calibrating separately the default intensity model to credit derivatives market data. A few variants of the model are calibrated in turn to market data, and different calibration procedures are compared. Numerical experiments show that the calibrated model can generate plausible volatility smiles. Hence, the model can be calibrated to a default swap term structure and few default swaptions, and the calibrated parameters can be used to value consistently other default swaptions (different strikes and maturities, or more complex structures) on the same credit reference name.Credit derivatives, credit default, swap, credit default swaption, jump-diffusion, stochastic intensity, doubly stochastic poisson process, cox process

A STRUCTURAL MODEL FOR CREDIT-EQUITY DERIVATIVES AND BESPOKE CDOs

We present a new structural model for single name equity and credit derivatives which we also correlate across reference names to produce a model for bespoke synthetic CDOs. The model captures volatility and outlook risk along with correlation risk for small and for large moves separately. We show that the model calibrates well to both equity structured products and credit derivatives. As examples, we discuss a number of single name derivatives on IBM spanning the credit-equity spectrum and ranging from volatility swaps, to cliquets, CDS options and CDSs on leveraged loans with pre-payment risk. We also use the model to price tranches on the investment grade DJ.CDX.IG index along with tranches on the high yield index DJ.CDX.HY. We show that the model gives consistent and high precision pricing across all these derivative asset classes. We show that this can be achieved consistently, with the very same parameter choices across these diverse derivative assets and making use of only minor explicit time dependencies.Credit derivatives; equity derivatives; long dated derivatives; CDOs; structural model

Modeling basket credit default swaps with default contagion

The specification of a realistic dependence structure is key to the pricing of multi-name credit derivatives. We value small kth-to-default CDS baskets in the presence of asset correlation and default contagion. Using a first-passage framework, firm values are modeled as correlated geometric Brownian motions with exponential default thresholds. Idiosyncratic links between companies are incorporated through a contagion mechanism whereby a default event leads to jumps in volatility at related entities. Our framework allows for default causality and is extremely flexible, enabling us to evaluate the spread impact of firm value correlations and credit contagion for symmetric and asymmetric baskets