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CDO With Stochastic Recovery
  • Pricing CDOs with State Dependent Stochastic Recovery Rates Up to the 2007 crisis, research within bottom-up CDO models mainly concentrated on the dependence between defaults. Since then, due to substantial increases in market prices of systemic credit risk protection, more attention has been paid to recovery rate assumptions. In this paper, we use stochastic orders theory to assess the impact of recovery on CDOs and show that, in a factor copula framework, a decrease of recovery rates leads to an increase of the expected loss on senior tranches, even though the expected loss on the portfolio is kept fixed. This result applies to a wide range of latent factor models and is not specific to the Gaussian copula model. We then suggest introducing stochastic recovery rates in such a way that the conditional on the factor expected loss (or equivalently the large portfolio approximation) is the same as in the recovery markdown case. However, granular portfolios behave differently. We show that a markdown is associated with riskier portfolios that when using the stochastic recovery rate framework. As a consequence, the expected loss on a senior tranche is larger in the former case, whatever the attachment point. We also deal with implementation and numerical issues related to the pricing of CDOs within the stochastic recovery rate framework. Due to differences across names regarding the conditional (on the factor) losses given default, the standard recursion approach becomes problematic. We suggest approximating the conditional on the factor loss distributions, through expansions around some base distribution. Finally, we show that the independence and comonotonic cases provide some easy to compute bounds on expected losses of senior or equity tranches. , Salah Amraoui, Laurent Cousot, Sébastien Hitier and Jean-Paul Laurent (2012)
  • Double Impact on CVA for CDS: Wrong-Way Risk with Stochastic Recovery Current CVA modeling framework has ignored the impact of stochastic recovery rate. Due to the possible negative correlation between default and recovery rate, stochastic recovery rate could have a doubling effect on wrong-way risk. In the case of a payer CDS, when counterparty defaults, the CDS value could be higher due to default contagion while the recovery rate may also be lower if the economy is in a downturn. Using our recently proposed model of correlated stochastic recovery in the default time Gaussian copula framework, we demonstrate this double impact on wrong-way risk in the CVA calculation for a payer CDS. We also present a new form of Gaussian copula that correlates both default time and recovery rate. , Hui Li (2010)
  • A Spot Recovery Rate Extension of the Gaussian Copula The market evolution since the end of 2007 has been characterized by an increase of the systemic risk and a high number of defaults. Realized recovery rates have been very dispersed and different from standard assumptions, while 60%-100% super-senior tranches on standard indices have started to trade with significant spread levels. This has triggered a growing interest for stochastic recovery modelling. This paper presents an extension to the standard Gaussian copula framework that introduces a consistent modelling of stochastic recovery. We choose to model directly the spot recovery, which allows to preserve time consistency, and compare this approach to the standard ones, defined in terms of recovery to maturity. Taking a specific form of the spot recovery function, we show that the model is flexible and tractable, and easy to calibrate to both individual credit spread curves and index tranche markets. Through practical numerical examples, we analyze specific model properties, focusing on default risk. , N.Bennani, J.Maetz (2009)
  • Stochastic Recovery Model Applicable to First-to-Default Basket Pricing We propose a stochastic recovery framework for single-factor copula models, an extension of the Krekel model. It allows for efficient pricing of collateralized debt obligations and first-to-default baskets consistently with single-name pricing. We analyze such properties like recovery markdown, recovery rate correlation and implied base correlations. The application to first-to-default pricing is described in detail, including the analysis of obtained par spreads and sensitivity to correlation. In the deterministic recovery case, we recover the Hull and White model. , Roman Werpachowski (2009)
  • Extension of Spot Recovery Model for Gaussian Copula Heightened systematic risk in the credit crisis has created challenges to CDO pricing and risk management. One important focus has been on the modeling of stochastic recovery. Different approaches within the Gaussian Copula framework have been proposed, but a consistent model was lacking until the recent paper of Bennani and Maetz [6] which shifted the modeling from period recovery to spot recovery. In this paper, we generalize their model to an arbitrary spot recovery distribution setup and extend the deterministic dependency on systematic factor to a random one. Besides, an extra parameter is introduced to control the correlation between default and recovery rate and the correlation between the recovery rates. , Li, Hui (2009)
  • On Models of Stochastic Recovery for Base Correlation This paper discusses various ways to add correlated stochastic recovery to the Gaussian Copula base correlation framework for pricing CDOs. Several recent models are extended to more general framework. It is shown that, conditional on the Gaussian systematic factor, negative forward recovery rate may appear in these models. This suggests that current static copula models of correlated default and recovery processes are inherently inconsistent. , Li, Hui (2009)
  • Cdo Mapping with Stochastic Recovery We discuss in detail the mapping methodology for the valuation of bespoke single tranche Collateralized Debt Obligations in the context of the stochastic recovery gaussian factor modelling framework recently proposed by Amraoui and Hitier (2008). , Andrea Prampolini, Matthias Dinnis (2009)
  • CDS and CDO Pricing with Stochastic Recovery , Charaf Ech-Chatbi (2008)
  • Pricing distressed CDOs with Base Correlation and Stochastic Recovery , M.Krekel (2008)
  • Optimal Stochastic Recovery for Base Correlation , S.Amraoui, S.Hitier (2008)





















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