Credit Models and the Crisis: A Journey into CDOs, Copulas, Correlations and Dynamic Models

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Introduction: Credit Modelling Pre- and In-Crisis

This book aims to show the limits of popular models or pseudo-models (mostly quoting mechanisms with modelling semblance) that, in recent years, have been extensively used to mark to market and risk manage multi-name credit derivatives. We present a compendium of results that we first published in 2006 before the crisis pointing out the dangers in the modelling paradigms used at the time in the market, and showing how the situation has even worsened subsequently by analysing more recent data. We also point out that the current paradigm had been heavily criticized before the crisis, referring to our work and the works of other authors addressing the main limitations of the current market paradigm well before popular accounts such as Salmon (2009) appeared. The problems of the current paradigm include:

• An unrealistic Gaussian Copula assumption and the flattening of 7750 pairwise dependence parameters into one.

• Lack of consistency of the implied correlation market models with more than one tranche quote at the time.

• Occasional impossibility of calibration even of single tranches, or possibility to obtain negative expected tranched losses violating the arbitrage-free constraints.

• Lack of an implied loss distribution consistent with market CDO tranche quotes for a single maturity.

• Lack of a loss distribution dynamics consistent with CDO tranche quotes on several maturities.

• Lack of credit spread volatility, resulting for example ...