Li, Yadong (2009): A Dynamic Correlation Modelling Framework with Consistent Stochastic Recovery.
This is the latest version of this item.
Download (289Kb) | Preview
This paper describes a flexible and tractable bottom-up dynamic correlation modelling framework with a consistent stochastic recovery specification. The stochastic recovery specification only models the first two moments of the spot recovery rate as the higher moments of the recovery rate have almost no contribution to the loss distribution and CDO tranche pricing. Observing that only the joint distribution of default indicators is needed to build the portfolio loss distribution, we argue that the default indicator copula should be used instead of the default time copula for the purpose of CDO tranche calibration and pricing. We then defined a generic class of default indicator copula with the "time locality" property, which makes it easy to calibrate to index tranche prices across multiple maturities.
This correlation modelling framework has the unique advantage that the joint distribution of default time and other dynamic properties of the model can be changed independently from the loss distribution and tranche prices. After calibrating the model to index tranche prices, existing top-down methods can be applied to the common factor process to construct very flexible systemic dynamics without changing the already calibrated tranche prices. This modelling framework therefore combines the best features of the bottom-up and top-down models: it is fully consistent with all the single name market information and it admits very rich and flexible spread dynamics.
Numerical results from a non-parametric implementation of this modelling framework are also presented. The non-parametric implementation achieved fast and accurate calibration to the index tranches across multiple maturities even under extreme market conditions. A conditional Markov chain method is also proposed to construct the systemic dynamics, which supports an efficient lattice pricing method for dynamic spread instruments. We also showed how to price tranche options as an example of this fast lattice method.
|Item Type:||MPRA Paper|
|Original Title:||A Dynamic Correlation Modelling Framework with Consistent Stochastic Recovery|
|Keywords:||Credit; Correlation; CDO; Dynamic; Copula; Stochastic Recovery; Bottom-up; Top-down|
|Subjects:||C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
D - Microeconomics > D4 - Market Structure and Pricing > D40 - General
|Depositing User:||Yadong Li|
|Date Deposited:||05. Feb 2010 11:33|
|Last Modified:||16. Feb 2013 06:37|
Amraoui, S. & S. Hitier. 2008. “Optimal Stochastic Recovery for Base Correlation.” defaultrisk.com .
Andersen, L. & J. Sidenius. 2004. “Extensions to the Gaussian Copula: Random Recovery and Random Factor Loadings.” Journal of Credit Risk .
Andersen, L., J. Sidenius & S. Basu. 2003. “All your hedges in one basket.” Risk .
Arnsdorf, M. & I. Halperin. 2007. “BSLP: Markovian Bivariate Spread-Loss Model for Portfolio Credit Derivatives.” defaultrisk.com .
Bennani, N. 2005. “The Forward Loss Model: A dynamic term structure approach for the pricing of portfolio credit derivatives.” defaultrisk.com .
Chapovsky, A., A. Rennie & P. Tavares. 2006. “Stochastic Intensity Modelling for Structured Credit Exotics.” defaultrisk.com .
Epple, F., S. Morgan & L. Schloegl. 2006. “Joint Distribution of Portfolio Losses and Exotic Portfolio Products.” Lehman Brothers: Quantitative Credit Research Quarterly pp. 44–55.
Giesecke, K. & L. Goldberg. 2005. “A Top-down approach to Multi-name Credit.” defaultrisk.com .
Halperin, I. & P. Tomecek. 2008. “Climbing Down from the Top: Single Name Dynamics in Credit Top Down Models.” defaultrisk.com .
Hull, J. & A. White. 2006. “Valuing Credit Derivatives Using an Impplied Copula Approach.” Journal of Derivatives .
Kogan, L. 2008. “A Dynamic Default Correlation Model.” Lehman Brothers: Quantitative Credit Research Quarterly .
Krekel, M. 2008. “Pricing Distressed CDOs with Base Correlation and Stochastic Recovery.” defaultrisk. com .
Li, D. 2000. “On Default Correlation: A Copula Function Approach.” Journal of Fixed Income .
Longstaff, F. & E. Schwartz. 2001. “Valuing American Options by Simulation: A Simple Least-squares Approach.” Review of Financial Studies .
Mortensen, A. 2006. “Semi-analytical Valuation of Basket Credit Derivatives in Intensity-Based Models.” defaultrisk.com .
O’Kane, D. & M. Livesey. 2004. “Base Correlation Explained.” Lehman Brothers: Quantitative Credit Research Quarterly pp. 3–20.
Schonbucher, P. 2006. “Portfolio Losses and the Term Structure of Loss Transition Rates: A new methodology for the pricing of portfolio derivatives.” defaultrisk.com .
Shelton, D. 2004. “Back to Normal.” Citigroup Global Structured Credit Research .
Sidenius, J. 2007. “On the Term Structure of Loss Distributions - a Forward Model Approach.” International Journal of Theoretical and Applied Finance .
Sidenius, J., V. Piterbarg & L. Andersen. 2006. “A New Framework for Dynamic Credit Portfolio Loss Modeling.” defaultrisk.com .
Skarke, H. 2005. “Remarks on Pricing Correlation Products.” defaultrisk.com .
Vacca, L. 2005. “Unbiased risk-neutral loss distributions.” Risk .
Available Versions of this Item
A Dynamic Correlation Modelling Framework with Consistent Stochastic Recovery. (deposited 30. Apr 2009 00:28)
- A Dynamic Correlation Modelling Framework with Consistent Stochastic Recovery. (deposited 05. Feb 2010 11:33) [Currently Displayed]