On cox processes and credit risky securities
- David Lando
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A framework is presented for modeling defaultable securities and credit derivatives which allows for dependence between market risk factors and credit risk. The framework reduces the technical issues of modeling credit risk to the same issues faced when modeling the ordinary term structure of interest rates. It is shown how to generalize a model of Jarrow, Lando and Turnbull (1997) to allow for stochastic transition intensities between rating categories and into default. This generalization can handle contracts with payments explicitly linked to ratings. It is also shown how to obtain a term structure model for all different rating categories simultaneously and how to obtain an affine-like structure. An implementation is given in a simple one factor model in which the affine structure gives closed form solutions.
- Artzner, P., Delbaen, F. (1995) Default Risk Insurance and Incomplete Markets. Mathematical Finance 5: pp. 187-195
- Black, F., Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy 3: pp. 637-654
- Cooper, I., Martin, M. (1996) Default Risk and Derivative Products. Applied Mathematical Finance 3: pp. 53-74
- Duffee, G. (1996) Treasury Yields and Corporate Bond Yields Spreads: An Empirical Analysis. Working Paper. Federal Reserve Board, Washington DC
- Duffie, D. (1992) Dynamic Asset Pricing Theory. Princeton University Press, Princeton
- Duffie, D., Huang, M. (1996) Swap Rates and Credit Quality. Journal of Finance 51: pp. 921-949
- Duffie, D. and K. Singleton. (1996). “Modeling Term Structures of Defaultable Bonds,” Working Paper, Stanford University.
- Duffie, D., Singleton, K. (1997) An Econometric Model of the Term Structure of Interest Rate Swap Yields. Journal of Finance 52: pp. 1287-1321
- Duffie, D., Schroder, M., Skiadas, C. (1996) Recursive Valuation of Defaultable Securities and the Timing of Resolution of Uncertainty. The Annals of Applied Probability 6: pp. 1075-1090
- Fons, J. and A. Kimball. (1991). “Corporate Bond Defaults and Default Rates 1970–1990,”The Journal of Fixed Income, 36–47.
- Gill, R., Johansen, S. (1990) A Survey of Product-Integration with a View Towards Applications in Survival Analysis. The Annals of Statistics 18: pp. 1501-1555
- Grandell, J. (1976) Doubly Stochastic Poisson Processes. Volume 529 ofLecture Notes in Mathematics. Springer, New York
- Jarrow, R., Lando, D., Turnbull, S. (1997) A Markov Model for the Term Structure of Credit Risk Spreads. Review of Financial Studies 10: pp. 481-523
- Jarrow, R., Turnbull, S. (1995) Pricing Options on Financial Securities Subject to Credit Risk. Journal of Finance 50: pp. 53-85
- Karatzas, I., Shreve, S. (1988) Brownian Motion and Stochastic Calculus. Springer, New York
- Lando, D. (1994). “Three Essays on Contingent Claims Pricing,” PhD Dissertation, Cornell University.
- Lando, D. (1997). “Modelling Bonds and Derivatives with Credit Risk.” In M. Dempster and S. Pliska (eds.),Mathematics of Financial Derivativcs, 369–393. Cambridge University Press.
- Longstaff, F., Schwartz, E. (1995) A Simple Approach to Valuing Risky Fixed and Floating Rate Debt. Journal of Finance 50: pp. 789-819
- Madan, D. and H. Unal. (1995). “Pricing the Risks of Default,” Working Paper, University of Maryland.
- Merton, R. C. (1974) On the Pricing of Corporate Debt: The Risk Structure of Interest Rates. Journal of Finance 2: pp. 449-470
- Williams, D. (1991).Probability with Martingales. Cambridge University Press.
- On cox processes and credit risky securities
Review of Derivatives Research
Volume 2, Issue 2-3 , pp 99-120
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- credit risk
- Cox process
- credit derivatives
- Industry Sectors
- David Lando (1)
- Author Affiliations
- 1. Department of Operations Research, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark