Optimal Stochastic Recovery for Base Correlation

Amraoui, Salah; Hitier, Sebastien

doi:10.2139/ssrn.2719672

Cited by 41 publications

(49 citation statements)

References 5 publications

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“…Subsection I.1 provides the conceptual framework to analyse such a markdown while subsection I.2 is devoted to numerical illustrations. -Section II recalls the stochastic recovery rate modelling framework introduced by Amraoui and Hitier [2008] and states some bounds and monotonicity results on the stochastic recovery rates. -Section III discusses the implementation and numerical issues related to the pricing of CDOs in the previous framework.…”

Section: Introductionmentioning

confidence: 99%

Pricing CDOs with state-dependent stochastic recovery rates

Amraoui

Cousot

Hitier

et al. 2012

Quantitative Finance

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Up to the 2007 crisis, research within bottom-up CDO models mainly concentrated on the dependence between defaults. However, due to the substantial increase in the market price of systemic credit risk protection, more attention has been paid to recovery rate assumptions. In this paper, we focus first on deterministic recovery rates in a factor copula framework. We use stochastic orders theory to assess the impact of a recovery markdown on CDOs and show that it 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. 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.

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Section: Introductionmentioning

confidence: 99%

Pricing CDOs with state-dependent stochastic recovery rates

Amraoui

Cousot

Hitier

et al. 2012

Quantitative Finance

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“…Base correlations are implied by the Gaussian copula model for the Lévy subordinator model prices. Model prices and hedge ratios are computed for tranches [0,3]%, [3,7]%, [7,10]%, [10,15]% and [15,30]%. As can be seen from the figures, despite having only two parameters at its disposal, the model is capable of generating correlation smiles of various slope characteristics.…”

Section: Discussionmentioning

confidence: 99%

“…Random recovery rates have been discussed by Andersen and Sidenius [2004], and recently by Amraoui and Hitier [2008] and Krekel [2008] in response to the recent crisis within the context of the Gaussian copula model. Here, let us consider a similar approach with an emphasis on tractability, and randomness of recovery rates arising from a decreasing dependence on F .…”

Section: Random Recovery Ratesmentioning

confidence: 99%

Levy Subordinator Model: A Two Parameter Model of Default Dependency

Balakrishna¹

2011

SSRN Journal

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“…. , n. To fix the ideas and without a lack of generality, we consider the particular couple of indices (1,2). In particular, the drift of dV t should be zero for trajectories where the Q it take very large or very small values, i = 1, 2.…”

Section: Proof Of Theoremmentioning

confidence: 99%

On Break-Even Correlation: The Way to Price Structured Credit Derivatives by Replication

Vigneron

Fermanian

2009

SSRN Journal

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We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient conditions so that the corresponding asset prices are martingales and introduce the concept of "break-even" correlation matrix. When no sudden jump-to-default events occur, we show that the perfect replication of these payoffs under the GCM is obtained if and only if the underlying single name credit spreads follow a particular family of dynamics. We calculate the corresponding break-even correlations and we exhibit a class of Merton-style models that are consistent with this result. We explain why the GCM does not have a lot of competitors among the class of one-period static models, except perhaps the Clayton copula.

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Optimal Stochastic Recovery for Base Correlation

Cited by 41 publications

References 5 publications

Pricing CDOs with state-dependent stochastic recovery rates

Pricing CDOs with state-dependent stochastic recovery rates

Levy Subordinator Model: A Two Parameter Model of Default Dependency

On Break-Even Correlation: The Way to Price Structured Credit Derivatives by Replication

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