of the Gaussian copula is the difficulty to calibrate it to market prices. In practice, typically a single correlation parameter (not a correlation matrix) is used to model the default correlation between any two entities in a collateralized debt obligation, CDO. Conceptually this correlation parameter should be the same for the entire CDO portfolio. However, traders randomly alter the correlation parameter for different tranches, in order to derive desired tranche spreads. Traders increase the correlation for ‘extreme’ tranches as the equity tranche or senior tranches, referred to as the correlation smile. This is similar to the often cited implied volatility smile in the Black–Scholes–Merton model. Here traders increase the implied volatility especially for out-of-the money puts, but also for out-of-the money calls to increase the option price.. In a mean-variance optimization framework, accurate estimation of the variance-covariance matrix is paramount. Thus, forecasting with Monte-Carlo simulation with the Gaussian copula and well-specified marginal distributions are effective. Allowing the modeling process to allow for empirical characteristics in stock returns such as auto-regression, asymmetric volatility, skewness, and kurtosis is important. Not accounting for these attributes lead to severe estimation error in the correlations and variances that have negative biases (as much as 70% of the true values). (c) Risk management A further criticism of the Copula approach is that the copula model is static and consequently allows only limited risk management, see Finger (2009) or Donnelly and Embrechts (2010). The original copulas models of Vasicek (1987) and Li (2000) and several extensions of the model as Hull and White (2004) or Gregory and Laurent (2004) do have a one period time horizon, i.e. are static. In particular, there is no stochastic process for the critical underlying variables default intensity and default correlation. However, even in these early copula formulations, back testing and stress testing the variables for different time horizons can give valuable sensitivities, see Whetten and Adelson (2004) and Meissner, Hector, and. Rasmussen (2008). In addition, the copula variables can be made a function of time as in Hull, Predescu, and White (2005). This still does not create a fully dynamic stochastic process with drift and noise, which allows flexible hedging and risk management. The best solutions are truly dynamic copula frameworks, see section ‘Dynamic Copulas’ below. Irrational complacency Before the global 2007–08 financial crisis, numerous market participants trusted the copula model uncritically and naively. However, the 2007–08 crisis was less a