Incorporating multi-dimensional tail dependencies in the valuation of credit derivatives
Noel McWilliam, Kar-Wei Loh, Huan Huang · Quantitative Finance · 2011
The need for an accurate representation of tail risk has become increasingly acute in the wake of the credit crisis. We introduce a hyper-cuboid normal mixture copula that permits the representation of complex tail-dependence structures in a multi-dimensional setting. We outline an efficient pattern-recognition calibration methodology that can identify tail dependencies independent of the number of risk factors considered. This model is used to develop a new framework for pricing credit derivative instruments, and we derive semi-analytical and analytical pricing formulae for a first-to-default swap and illustrate with an example valuation. Model assumptions are validated against iTraxx Series 5 equity data over an 8-year period. Identification and representation of tail dependencies is crucial to further the study of contagion dynamics, and our model provides a basis for future research in this area.