Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-28T00:29:31.676Z Has data issue: false hasContentIssue false
  • English
  • Français

A Note on Credit Insurance

Published online by Cambridge University Press:  17 April 2015

Johannes Leitner
Johannes Leitner*
Affiliation:
Research Unit for Financial and Actuarial Mathematics, Institute for Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstraße 8-10/105, A-1040 Vienna, Austria. E-mail: jleitner@fam.tuwien.ac.at
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In a simple stationary setting with constant interest rate, we derive pricing formulas for defaultable bonds with stochastic recovery rate using a replication argument. Replication is done by using an insurance contract (i.e. a kind of credit default swap), the price of which is determined by a dynamic premium calculation principle. We consider two cases, a linear one, where pricing amounts to solving an inhomogeneous linear ODE, and a super-linear case where a Riccati ODE has to be solved.

Keywords

Credit insurancecredit default swapsrandom measuresterm structure for defaultable bondsdynamic premium calculation principle
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 36 , Issue 2 , November 2006 , pp. 347 - 360
Copyright
Copyright © ASTIN Bulletin 2006

References

Artzner, P., Delbaen, F., Eber, J.-M. and Heath, D. (1999) Coherent Measures of Risk. Mathematical Finance 9 203–228.CrossRefGoogle Scholar
Bielecki, T. and Rutkowski, M. (2002) Credit Risk: Modeling, Valuation and Hedging. Springer Finance, Vol. 89. Springer: Berlin.Google Scholar
Brémaud, P. (1981) Point processes and queues, martingale dynamics. Springer Series in Statistics. Springer: New York.CrossRefGoogle Scholar
Brémaud, P. and Jacod, J. (1977) Processus ponctuels et martingales: Résultats récents sur la modélisation et le filtrage. Advances in Applied Probability 9, 362--416.CrossRefGoogle Scholar
Chou, C.-S. and Meyer, P.A. (1974) La représentation des martingales relatives à un processus punctuel discret. Comptes Rendus de l’Académie des Sciences de Paris, Série A278, 1561–1563.Google Scholar
Davis, M.H.A. (1976) The Representation of Martingales of Jump Processes. SIAM Journal of Control and Optimization 14(4), 623–638.CrossRefGoogle Scholar
Delbaen, F. and Schachermayer, W. (1994) Ageneral version of the fundamental theorem of asset pricing. Mathematische Annalen 300, 463–520.CrossRefGoogle Scholar
Delbaen, F., Monat, P., Schachermayer, W., Schweizer, M. and Stricker, C. (1997) Weighted norm inequalities and hedging in incomplete markets. Finance and Stochastics 1, 181–227.CrossRefGoogle Scholar
Delbaen, F., Grandits, P., Rheinländer, T., Samperi, D., Schweizer, M. and Stricker, C. (2002) Exponential hedging and entropic penalties. Mathematical Finance 12, 99–123.CrossRefGoogle Scholar
Duffie, D. and Singleton, K. (2003) Credit Risk: Pricing, Measurement and Management. Princeton University Press: Princeton and Oxford.CrossRefGoogle Scholar
Föllmer, H. and Schied, A. (2002) Stochastic Finance. Berlin: de Gruyter.CrossRefGoogle Scholar
Frittelli, M. (2000) The minimal entropy martingale measure and the valuation problem in incomplete markets. Mathematical Finance 10, 39–52.CrossRefGoogle Scholar
Gerber, H.U. (1979) An Introduction to Mathematical Risk Theory. Huebner Foundation Monographs. University of Pennsylvania.Google Scholar
Goovaerts, M., Kaas, R., Dhaene, J. and Tang, Q. (2003) Aunified approach to generate risk measures. ASTIN Bulletin, 33(2), 173–191.CrossRefGoogle Scholar
Jacod, J. (1975) Multivariate Point Processes: Predictable Projection, Radon-Nikodym Derivatives, Representation of Martingales. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 31, 235–253.CrossRefGoogle Scholar
Jacod, J. and Shiryaev, A.N. (1987) Limit Theorems for Stochastic Processes. Springer: Berlin.CrossRefGoogle Scholar
Jeanblanc, M. and Rutkowski, M. (2000) Modelling of default risk: an overview. In: Mathematical Finance: Theory and Practice, p. 171–269. Higher Education Press: Beijing.Google Scholar
Kramkov, D. and Schachermayer, W. (1999) The asymptotic elasticity of utility functions and optimal investment in incomplete markets. Annals of Applied Probability 9(3), 904–950.CrossRefGoogle Scholar
Lando, D. (2004) Cedit Risk Modelling: Theory and Applications. Princeton University Press: Princeton, New Jersey.CrossRefGoogle Scholar
Last, G. and Brandt, A. (1995) Marked Point Processes on the Real Line. Springer: Berlin.Google Scholar
Leitner, J. (2005) Event Insurance Markets. Submitted.Google Scholar
Liptser, R. and Shiryaev, A.N. (2000) Statistics of random processes II. Applications. Applications of Mathematics. Stochastic modelling and applied probability 6. Springer: Berlin.Google Scholar
Mikosch, T. (2004) Non-Life Insurance Mathematics. Springer: Berlin.Google Scholar
Schachermayer, W. (2001) Optimal investment in incomplete markets when wealth may become negative. Annals of Applied Probability 11(3), 694–734.CrossRefGoogle Scholar
Wang, S. (1996) Premium Calculation by Transforming the Layer Premium Density. ASTIN Bulletin 26(1), 71–92.CrossRefGoogle Scholar