Pricing and Risk Management of Synthetic CDOs
This book considers the one-factor copula model for credit portfolios that are used for pricing synthetic CDO structures as well as for risk management and measurement applications involving the generation of scenarios for the complete universe of risk factors and the inclusion of CDO structures in a portfolio context. For this objective, it is especially important to have a computationally fast model that can also be used in a scenario simulation framework. The well known Gaussian copula model is extended in various ways in order to improve its drawbacks of correlation smile and time inconsistency. Also the application of the large homogeneous cell assumption, that allows to differentiate between rating classes, makes the model convenient and powerful for practical applications. The Crash-NIG extension introduces an important regime-switching feature allowing the possibility of a market crash that is characterized by a high-correlation regime.
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absolute error asset return banks base correlation bonds calibration CDO tranches CDS indices computed Crash-NIG copula model credit default swaps credit derivative contract credit derivatives credit event credit instruments credit risk credit spread CVaR default intensity default probability denote different maturities distribution function double-t equity tranche expected loss factor copula model factor Gaussian Gaussian copula model Hidden Markov Model implied correlation Inverse Gaussian distribution investors iTraxx Europe iTraxx index iTraxx spread iTraxx tranches kurtosis large homogeneous portfolio Lemma liquidity loans log-normal Lognormal spread market factor market quotes Markov matrix mortgage NIG copula model NIG distribution NIG model normal spread notional amount optimization payments premium pricing protection buyer protection seller random variables rating cells rating migration reference entity securitisation securitization senior tranche simulation skewness stochastic process sub-prime crisis Synthetic CDOs Table term-structure Vasicek model Wiener process zero