A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part II: Common-Shock Interpretation, Calibration and Hedging issues
نویسندگان
چکیده
In this paper, we prove that the conditional dependence structure of default times in the Markov model of [4] belongs to the class of Marshall-Olkin copulas. This allows us to derive a factor representation in terms of “common-shocks”, the latter beeing able to trigger simultaneous defaults in some pre-specified groups of obligors. This representation depends on the current default state of the credit portfolio so that fast convolution pricing schemes can be exploited for pricing and hedging credit portfolio derivatives. As emphasized in [4], the innovative breakthrough of this dynamic bottomup model is a suitable decoupling property between the dependence structure and the default marginals as in [10] (like in static copula models but here in a full-flesh dynamic “Markov copula” model). Given the fast deterministic pricing schemes of the present paper, the model can then be jointly calibrated to single-name and portfolio data in two steps, as opposed to a global joint optimization procedures involving all the model parameters at the same time which would be untractable numerically. We illustrate this numerically by results of calibration against market data from CDO tranches as well as individual CDS spreads. We also discuss hedging sensitivities computed in the models thus calibrated.
منابع مشابه
A Bottom-Up Dynamic Model of Portfolio Credit Risk. Part I: Markov Copula Perspective
We consider a bottom-up Markovian copula model of portfolio credit risk where instantaneous contagion is possible in the form of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula set-up. In this sense this model solves the bottom...
متن کاملDynamic Modeling of Portfolio Credit Risk with Common Shocks
We consider a bottom-up Markovian model of portfolio credit risk where dependence among credit names stems from the possibility of simultaneous defaults. A common shocks interpretation of the model is possible so that efficient convolution recursion procedures are available for pricing and hedging CDO tranches, conditionally on any given state of the Markov model. Calibration of marginals and d...
متن کاملDynamic Hedging of Portfolio Credit Risk in a Markov Copula Model
We consider a bottom-up Markovian copula model of portfolio credit risk where dependence among credit names mainly stems from the possibility of simultaneous defaults. Due to the Markovian copula nature of the model, calibration of marginals and dependence parameters can be performed separately using a two-steps procedure, much like in a standard static copula set-up. In addition, the model adm...
متن کاملDynamic Hedging of Portfolio Credit Derivatives
We compare the performance of various hedging strategies for index collateralized debt obligation (CDO) tranches across a variety of models and hedging methods during the recent credit crisis. Our empirical analysis shows evidence for market incompleteness: a large proportion of risk in the CDO tranches appears to be unhedgeable. We also show that, unlike what is commonly assumed, dynamic model...
متن کاملA Bottom-Up Dynamic Model of Portfolio Credit Risk with Stochastic Intensities and Random Recoveries
In [5], the authors introduced a Markov copula model of portfolio credit risk where pricing and hedging can be done in a sound theoretical and practical way. Further theoretical backgrounds and practical details are developped in [6] and [7] where numerical illustrations assumed deterministic intensities and constant recoveries. In the present paper, we show how to incorporate stochastic defaul...
متن کامل