A STRUCTURAL MODEL FOR CREDIT-EQUITY DERIVATIVES AND BESPOKE CDOs

Albanese, Claudio and Vidler, Alicia (2007): A STRUCTURAL MODEL FOR CREDIT-EQUITY DERIVATIVES AND BESPOKE CDOs. Published in: Wilmott Magazine , Vol. 2007, No. May (1 May 2007)

Abstract

We present a new structural model for single name equity and credit derivatives which we also correlate across reference names to produce a model for bespoke synthetic CDOs. The model captures volatility and outlook risk along with correlation risk for small and for large moves separately. We show that the model calibrates well to both equity structured products and credit derivatives. As examples, we discuss a number of single name derivatives on IBM spanning the credit-equity spectrum and ranging from volatility swaps, to cliquets, CDS options and CDSs on leveraged loans with pre-payment risk. We also use the model to price tranches on the investment grade DJ.CDX.IG index along with tranches on the high yield index DJ.CDX.HY. We show that the model gives consistent and high precision pricing across all these derivative asset classes. We show that this can be achieved consistently, with the very same parameter choices across these diverse derivative assets and making use of only minor explicit time dependencies.

• Item Type: MPRA Paper
• Institution: Independent Consultant
• Language: English
• Keywords: Credit derivatives; equity derivatives; long dated derivatives; CDOs; structural model
• Subjects: G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing

References

Albanese, C. (2006). Operator Methods, Abelian Path Dependents and Dynamic Conditioning. preprint. Albanese, C. and O. Chen (2004). Implied migration rates from credit barrier model. The Journal of Banking and Finance, to appear. Albanese, C. and O. Chen (2005a). Credit barrier models in a discrete framework. Contemporary Mathematics 351, Mathematical Finance pp. 1–11. Albanese, C. and O. Chen (2005b). Discrete credit barrier models. Quantitative Finance 5, 247– 256. Albanese, C., J. Campolieti, O. Chen and A. Zavidonov (2003). Credit barrier models. Risk 16(6), 109–113. Albanese, C., O. Chen, A. Dalessandro and A. Vidler (2005-2006). Dynamic Credit Correlation Modelling. preprint. Andersen, Leif and Jakob Sidenius (2004). Extensions to the gaussian copula: random recovery and random factor loadings. Journal of Credit Risk 1, 1:29. Bratteli, O. and D.W. Robinson (2002). Operator algebras and quantum statistical mechanics. Vol. 1 and 2. Springer. di Graziano, G. and C. Rogers (n.d.). A Dynamic Approach to the Modelling of Correlation Credit Derivatives Using Markov Chains. preprint, Cambridge University. Giesecke, Kay and Lisa Goldberg (2005). A top down approach to multi-name credit. Working paper, Cornell University. Goto, Kazushige and Robert van de Geijn (to appear). Anatomy of High-Performance Matrix Multiplication. ACM Trans. Math. Soft. Hull, John and Alan White (2003). Valuation of a cdo and an n-th to-default cds without monte carlo simulation. Working paper, University of Toronto. Joshi, Mark S. and Alan Stacey (2005). Intensity gamma: a new approach to pricing portfolio credit derivatives. Working paper, Royal Bank of Scotland. Li, David. X. (2000). On default correlation: A copula function approach. working paper 99-07, Risk Metrics Group. Lucas, A., P. Klaassen, P. Spreij and S. Staetmans (2001). An analytic approach to credit risk of large corporate bond and loan portfolios. Journal of Banking and Finance 9, 1635–1664. O’Kane, D. and M. Livesey (2004). Base correlation explained. QCR Quarterly Q3/4, Lehman Brothers Fixed Income Quantitative Research. Schonbucher, P. (2006). Portfolio losses and the term structure of loss transition rates: a new methodology for the pricing of portfolio credit derivatives. Working paper, ETHZ. Trefethen, Lloyd N. and Mark Embree (2006). Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.