Credit Derivatives in an Affine Framework
Tóm tắt
An efficient method for valuing credit derivatives based on three entities is developed in an affine framework. This includes interdependence of market and credit risk, joint credit migration and counterparty default risk of three firms. As an application we provide closed form expressions for the joint distribution of default times, default correlations, and default swap spreads in the presence of counterparty default risk.
Tài liệu tham khảo
Artzner P., Delbaen F. (1995). Default risk and incomplete insurance markets. Mathematical Finance 5: 187–195
Bielecki, T. R., & Rutkowski, M. (2002). Credit risk: Modeling, valuation and hedging. Springer.
Birkhoff G., Rota G.C. (1989). Ordinary differential equations (4th ed). New York, John Wiley & Sons Inc.
Chen L., Filipović D. (2005). A simple model for credit migration and spread curves. Finance and Stochastics 9: 211–231
Chen, L., & Filipović, D. (2006). Credit derivatives in an affine framework (Working Paper Version), Working Paper.
Cheridito P., Filipović D., Kimmel R. (2007). Market price of risk specifications for affine models: theory and evidence. Journal of Financial Economics 83: 123–170
Cheridito P., Filipović D., Yor M. (2005). Equivalent and absolutely continous measure changes for jump-diffusion processes. The Annals of Applied Probability 15: 1713–1732
Crosbie, P. J., & Bohn, J. R. (2003). Modeling default risk. Working paper, Moody’s and KMV.
Davis M., Lo V. (2001). Infectious defaults. Quantitative Finance 1: 382–386
Duffie D. (2004). Credit risk modeling with affine processes. Cattedra Galileiana, Scuola Normale Superiore, Pisa
Duffie D., Filipović D., Schachermayer W. (2003). Affine processes and applications in finance. The Annals of Applied Probability 13: 984–1053
Duffie D., Gârleanu N. (2001). Risk and valuation of collateralized debt obligations. Financial Analysts Journal 57: 41–59
Duffie D., Pan J., Singleton K. (2000). Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68: 1343–1376
Duffie D., Singleton K. (2003). Credit risk: Pricing, measurement, and management. Princeton University Press
Hull J., White A. (2000). Valuing credit default Swaps I: No counterparty default risk. The Journal of Derivatives 1: 29–40
Hull J., White A. (2001). Valuing credit default Swaps II: Modeling default correlations. The Journal of Derivatives 8: 12–22
Jarrow R., Yu F. (2001). Counterparty risk and the pricing of defaultable securities. Journal of Finance 56: 1765–1799
Lando D. (1998). On Cox processes and credit-risky securities. Review of Derivatives Research 2: 99–120
Lando, D. (2004). Credit risk modeling : Theory and applications. Princeton University Press.
McNeil, A. J., Frey, R., & Embrechts, P. (2005). Quantitative risk management: Concepts, techniques, and tools. Princeton University Press.
Schönbucher, P. (2003). Credit derivatives pricing models: Model, pricing and implementation. John Wiley & Sons.
Schönbucher, P., & Schubert, D. (2001). Copula-dependent default risk in intensity models. Working paper. Bonn University.
Singleton K., Umantsev L. (2002). Pricing coupon-bond options and swaptions in affine term structure models. Mathematical Finance 12: 427–446
Yu F. (2005). Correlated defaults in reduced-form models. Journal of Investment Management 3: 33–42