Abstract
We propose a reduced-form credit risk model where default intensities, interest rates and risk premia are determined by a not fully observable factor process with affine dynamics. The inclusion of latent factors enriches the model flexibility and induces an information-driven contagion effect among defaults of different issuers. The information on the unobserved factors is dynamically updated via stochastic filtering, on the basis of market data as well as rating scores. This allows for a continuous tuning of the model to the actual (latent) situation of the economy and provides a coherent and unified approach to pricing and risk management.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
- 2.
As shown in Sect. 2.2 of [14], more general credit risky products such as coupon-bearing corporate bonds and CDS spreads can be expressed by means of these elementary building blocks.
- 3.
- 4.
- 5.
- 6.
Notice that the observations are linear in X t but not all of them are affected by noise factors. Consequently, it may happen that the original filtering problem for (X t , Y t ) turns out to be degenerate. Furthermore, the auxiliary state process Z t has in general a lower dimension than the process X t .
- 7.
References
Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Prentice-Hall, Englewoods Cliffs (1979)
Azizpour, S., Giesecke, K.: Self-exciting corporate defaults: contagion vs. frailty. Working paper, Stanford University (2008)
Bhar, R., Chiarella, C., Runggaldier, W.J.: Inferring the forward looking equity risk premium from derivatives prices, Stud. Nonlinear Dyn. Econom. 8(1), article 3 (2004)
Bhar, R., Handzic, N.: A multifactor model of credit spreads, to appear in: Asia-Pac. Financ. Markets (2010)
Cheridito, P., Filipović, D., Kimmel, R.L.: Market price of risk specifications for affine models: Theory and Evidence, J. Finan. Econ. 83, 123–170 (2007)
Christensen, J.H.E., Hansen, E., Lando, D.: Confidence sets for continuous-time rating transition probabilities, J. Bank. and Finance 28, 2575–2602 (2004)
Dai, Q., Singleton, K.J.: Specification analysis of affine term structure models, J. Finance 55(5), 1943–1978 (2000)
Das, S.R., Duffie, D., Kapadia, N., Saita, L.: Common failings: how corporate defaults are correlated, J. Finance 62(1), 93–117 (2007)
Denault, M., Gauthier, G., Simonato, J.G.: Estimation of physical intensity models for default risk, J. Futures Mark. 29(2), 95–113 (2009)
Duffee, G.R.: Term premia and interest rate forecasts in affine models, J. Finance 57(1), 405–443 (2002)
Duffie, D., Eckner, A., Horel, G., Saita, L.: Frailty correlated default, J. Finance 64(5), 2089–2123 (2009)
Duffie, D., Kan, R.: A yield-factor model of interest rates, Math. Finance 6(4), 379–406 (1996).
Fontana, C.: Affine multi-factor credit risk models under incomplete information: filtering and parameter estimation. Thesis, University of Padova (2007)
Fontana, C., Runggaldier, W.J.: Credit risk and incomplete information: filtering and EM parameter estimation, Int. J. Theor. Appl. Finance 13(5), 683–715 (2010)
Hilscher, J., Wilson, M.: Credit ratings and credit risk. Working paper, Brandeis University and University of Oxford (2010)
Jarrow, R.A., Lando, D., Yu, F.: Default risk and diversification: theory and empirical implications, Math. Finance 15(1), 1–26 (2005)
Koopman, S.J., Lucas, A., Schwaab, B.: Macro, frailty and contagion effects in defaults: lessons from the 2008 credit crisis. Working paper, VU University Amsterdam (2010)
Koopman, S.J., Lucas, A., Schwaab, B.: Modeling frailty-correlated defaults using many macroeconomic covariates. Working paper, VU University Amsterdam (2010)
Korolkiewicz, M.W., Elliott, R.J.: A hidden Markov model of credit quality, J. Econom. Dynam. Control 32, 3807–3819 (2008)
McNeil, A.J., Frey, R., Embrechts, P.: Quantitative Risk Management. Princeton University Press, Princeton (2005)
Protter, P.E.: Stochastic Integration and Differential Equations, second edition, version 2.1. Springer, Berlin-Heidelberg-New York (2005)
Runggaldier, W.J.: Estimation via stochastic filtering in financial market models, Contemp. Math. 351, 309–318 (2004)
Schönbucher, P.J.: Information-driven default contagion. Working paper, Department of Mathematics, ETH Zürich (2003)
Yu, F.: Default correlation in reduced-form models, J. Invest. Manag. 3(4), 33–42 (2005)
Acknowledgements
I am thankful to Professor Wolfgang J. Runggaldier for valuable comments that helped to improve the paper. Financial support from the international “Nicola Bruti-Liberati” scholarship for studies in Quantitative Finance is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Italia
About this chapter
Cite this chapter
Fontana, C. (2012). Credit risk and incomplete information: A filtering framework for pricing and risk management. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Milano. https://doi.org/10.1007/978-88-470-2342-0_23
Download citation
DOI: https://doi.org/10.1007/978-88-470-2342-0_23
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-2341-3
Online ISBN: 978-88-470-2342-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)