Credit risk and contagion via self-exciting default intensity
Tóm tắt
Recent empirical evidences indicate that default rates are influenced not only by the observable or latent risk factors, but also depend on the history of past defaults. Motivated by this empirical finding, we consider in this paper a reduced-form, intensity-based credit risk model, which allows for both frailty and default contagion, using a so-called “self-exciting” intensity, in the sense that the default intensity varies not only with the risk factors, but also depends on the previous default history of all the firms. With “self-exciting” default intensity, we are able to obtain closed-form expressions for the pricing of credit derivative securities in our model. The estimation of parameters using the EM algorithm is considered as well.
Tài liệu tham khảo
Azizpour, S., Giesecke, K., Schwenkler, G.: Exploring the Sources of Default Clustering. Working paper, Stanford University (2014)
Bielecki, T.R., Rutkowski, M.: Credit Risk: Modeling, Valuation and Hedging. Springer, Berlin (2002)
Black, F., Cox, J.C.: Valuing corporate securities: some effects of bond indenture provisions. J. Finance 31(2), 351–367 (1976)
Collin-Dufresne, P., Goldstein, R., Helwege, J.: Is Credit Event Risk Priced? Modeling Contagion Via the Updating of Beliefs. Preprint, Carnegie Mellon University (2003)
Cvitanić, J., Ma, J., Zhang, J.: Laws of large numbers for self-inciting correlated defaults. Stoch Process Appl 122, 2781–2810 (2011)
Das, S.R., Duffie, D., Kapadia, N., Saita, L.: Common failings: how corporate defaults are correlated. J. Finance 62(1), 93–117 (2007)
Duffie, D., Lando, D.: Term structure of credit spreads with incomplete accounting information. Econometrica 69, 633–664 (2001)
Duffie, D., Singleton, K.: An econometric model of the term structure of interest-rate swap yields. J Financ 52(4), 1287–1321 (1997)
Duffie, D., Singleton, K.: Modeling term structures of defaultable bonds. Rev Financ Stud 12, 687–720 (1999)
Duffie, D., Singleton, K.: Credit Risk: Pricing, Measurement and Management. Princeton University Press, Princeton (2003)
Duffie, D., Eckner, A., Horel, G., Saita, L.: Frailty correlated default. J Financ 64, 2089–2123 (2009)
Elliott, R.J., Aggoun, L., Moore, J.B.: Hidden Markov models: Estimation and control. Applications of Mathematics (New York), 29, Springer, New York, xii+361 pp (1995)
Frey, R., Runggaldier, W.: Pricing credit derivatives under incomplete information: a nonlinear filtering approach. Financ Stochast 14, 495–526 (2010)
Frey, R., Schmidt, T.: Pricing and hedging of credit derivatives via the innovations approach to nonlinear filtering. Financ Stochast 16, 105–133 (2012)
Giesecke, K., Longstaff, F., Schaefer, S., Strebulaev, I.: Corporate bond default risk: a 150-year perspective. J Financ Econ 102, 233–250 (2011)
Giesecke, K., Longstaff, F., Schaefer, S., Strebulaev, I.: Macroeconomic effects of corporate default crises: a long-term perspective. J Financ Econ 111, 297–310 (2014)
Giesecke, K., Schwenkler, G.: Filtered likelihood for point processes. Working paper. Stanford University (2014)
Giesecke, K., Spiliopoulos, K., Sowers, R.: Default clustering in large portfolios: typical events. Ann Appl Probab 23(1), 348–385 (2013)
Hajek, B., Wong, E.: Stochastic Processes in Engineering Systems. Springer, Berlin (1985)
Jarrow, R.A., Turnbull, S.M.: Pricing derivatives on financial securities subject to credit risk. J Financ 50, 53–86 (1995)
Jarrow, R.A., Lando, D., Turnbull, S.M.: A Markov model for the term structure of credit risk spreads. Rev Financ Stud 10(2), 481–523 (1997)
Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Springer, Berlin (1988)
Merton, R.C.: On the pricing of corporate debt the risk structure of interest rates. J. Finance 29(2), 449–470 (1974)
Schönbucher, P.: The term structure of defaultable bond prices. Rev Deriv Res 2, 161–192 (1998)
Schönbucher, P.: Information Driven Default Contagion. Working Paper, ETH, Zurich (2003a)
Schönbucher, P.: Credit Derivatives Pricing Models: Models, Pricing and Implementation. Wiley, Chichester (2003b)