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Incorporating Multidimensional Tail Dependencies In The Valuation of Credit Derivatives May 15, 2009 05:51 PM GMT

This article highlights the importance of tail identification within a multi-dimensional setting, with a view to the wider problem of contagion modelling. As it shows, there is a substantial impact on the pricing of a first-to-default swap.
The causes for the credit crisis are multiple, from the broader economic spectrum (aggressive lending practices, unrealistic projections of underlying asset values, etc.) to specific market issues. However, one item is certain: broad securitization of certain credit instruments introduced a significantly new element of risk that was not adequately modelled or planned for. Recent events have served well to highlight the disastrous consequences of inadequate in-house risk management systems and the models upon which they rely.
The genesis of the current downturn can, at least in part, be attributed to a fundamental mis-pricing of credit derivative instruments in a way that ignored the complexities of extreme-value (or "tail") dependencies. In the wake of the credit crisis the resulting, immediately identifiable need is for a robust and accurate representation of this form of extreme-value risk. Considering the aggressive securitization of the market, the process by which extreme risk propagates within and between risk factors, otherwise known as contagion, takes on particular significance.
While a truthful representation of extreme values is of importance in the assessment of risk across all asset classes, it is especially relevant to the pricing of credit instruments since defaults can themselves be thought of as extreme events. As such the real value of contracts referencing multiple creditors will critically depend on their co-relationship in the tails of return distributions. Unfortunately popular asset-based credit derivative models are ignorant of the notion of multiple tail risks with the most widely used Gaussian framework ...

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