Modeling the Dynamics of Credit Spreads with Stochastic Volatility

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(1)2003s-51. Modeling the Dynamics of Credit Spreads with Stochastic Volatility Kris Jacobs, Xiaofei Li. Série Scientifique Scientific Series. Montréal Août 2003. © 2003 Kris Jacobs, Xiaofei Li. Tous droits réservés. All rights reserved. Reproduction partielle permise avec citation du document source, incluant la notice ©. Short sections may be quoted without explicit permission, if full credit, including © notice, is given to the source..

(2) CIRANO Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies du Québec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisationsmembres, d’une subvention d’infrastructure du ministère de la Recherche, de la Science et de la Technologie, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO is a private non-profit organization incorporated under the Québec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the Ministère de la Recherche, de la Science et de la Technologie, and grants and research mandates obtained by its research teams. Les organisations-partenaires / The Partner Organizations PARTENAIRE MAJEUR . Ministère du développement économique et régional [MDER] PARTENAIRES . Alcan inc. . Axa Canada . Banque du Canada . Banque Laurentienne du Canada . Banque Nationale du Canada . Banque Royale du Canada . Bell Canada . Bombardier . Bourse de Montréal . Développement des ressources humaines Canada [DRHC] . Fédération des caisses Desjardins du Québec . Gaz Métropolitain . Hydro-Québec . Industrie Canada . Ministère des Finances [MF] . Pratt & Whitney Canada Inc. . Raymond Chabot Grant Thornton . Ville de Montréal . École Polytechnique de Montréal . HEC Montréal . Université Concordia . Université de Montréal . Université du Québec à Montréal . Université Laval . Université McGill ASSOCIÉ À : . Institut de Finance Mathématique de Montréal (IFM 2) . Laboratoires universitaires Bell Canada . Réseau de calcul et de modélisation mathématique [RCM 2] . Réseau de centres d’excellence MITACS (Les mathématiques des technologies de l’information et des systèmes complexes) Les cahiers de la série scientifique (CS) visent à rendre accessibles des résultats de recherche effectuée au CIRANO afin de susciter échanges et commentaires. Ces cahiers sont écrits dans le style des publications scientifiques. Les idées et les opinions émises sont sous l’unique responsabilité des auteurs et ne représentent pas nécessairement les positions du CIRANO ou de ses partenaires. This paper presents research carried out at CIRANO and aims at encouraging discussion and comment. The observations and viewpoints expressed are the sole responsibility of the authors. They do not necessarily represent positions of CIRANO or its partners.. ISSN 1198-8177.

(3) Modeling the Dynamics of Credit Spreads with Stochastic Volatility* Kris Jacobs†, Xiaofei Li‡. Résumé / Abstract 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. Mots clés : risque de crédit; écarts de crédit; modèles à forme réduite; volatilité stochastique.. 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 fourfactor 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. Keywords: credit risk, credit spreads, reduced form models, stochastic volatility. Codes JEL : G12 *. Kris Jacobs would like to thank FCAR, SSHRC, IFM2 and CIRANO for financial support. We would like to thank Peter Christoffersen, Jan Ericsson and Jean-Guy Simonato for very helpful conversations and comments. † Associate Professor of Finance, McGill University and CIRANO. Faculty of Management, McGill University, 1001 Sherbrooke Street West, Montreal, Canada, H3A 1G5, tel. (514) 398-4025, fax: (514) 398-3876, email: [email protected]. ‡ Ph.D. Candidate, McGill University..

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