Financial correlation

Third, a zero Pearson product-moment correlation coefficient does not necessarily mean independence, because only the two first moments are considered.

Accurately estimating correlations requires the modeling process of marginals to incorporate characteristics such as skewness and kurtosis.

Not accounting for these attributes can lead to severe estimation error in the correlations and covariances that have negative biases (as much as 70% of the true values).

[3] In a practical application in portfolio optimization, 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.

In finance, copulas are typically applied to derive correlated default probabilities in a portfolio,[according to whom?]

Numerous non-academic articles have been written demonizing the copula approach and blaming it for the 2007/2008 global financial crisis, see for example Salmon 2009,[11] Jones 2009,[12] and Lohr 2009.

[13] There are three main criticisms of the copula approach: (a) tail dependence, (b) calibration, (c) risk management.

Hence it would be desirable to apply a correlation model with high co-movements in the lower tail of the joint distribution.

It can be mathematically shown that the Gaussian copula has relative low tail dependence, as seen in the following scatter plots.

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).

[24] In addition, the copula variables can be made a function of time as in Hull, Predescu, and White (2005).

[25] This still does not create a fully dynamic stochastic process with drift and noise, which allows flexible hedging and risk management.

Before the global 2007–08 financial crisis, numerous market participants trusted the copula model uncritically and naively.

[citation needed] However, the 2007–08 crisis was less a matter of a particular correlation model, but rather an issue of "irrational complacency".

[citation needed] The prime example is AIG's London subsidiary, which had sold credit default swaps and collateralized debt obligations in an amount of close to $500 billion without conducting any major hedging.

[26] In particular, if any credit correlation model is fed with benign input data as low default intensities and low default correlation, the risk output figures will be benign, ‘garbage in garbage out’ in modeling terminology.

[28] The "dynamic conditioning" approach models the evolution of multi-factor super-lattices, which correlate the return processes of each entity at each time step.

Binomial dynamic copulas apply combinatorial methods to avoid Monte Carlo simulations.

Richer dynamic Gaussian copulas apply Monte Carlo simulation and come at the cost of requiring powerful computer technology.

In order to avoid specifying the default correlation between each entity pair in a portfolio a factorization is often applied.

It was the de facto market model for pricing CDOs before the 2007/2008 global financial crisis.

, sometimes interpreted as the asset value of i, see Turc, Very, Benhamou and Alvarez et al. (2005),[29][better source needed] is also n~(0,1).

[citation needed] As of 2010, the OFGC is the basis for credit risk management in Basel II.

As discussed in section 2.3, in the CID framework, correlation is modeled by conditioning on a common market factor M, which impacts all entities to the same degree.

See the papers of Davis and Lo (2001)[30] and Jarrow and Yu (2001),[31] who pioneered contagion default modeling.

Although seemingly important information such as the default intensities of individual entities is disregarded, a top-down model can typically better capture properties of the portfolio such as volatility or correlation smiles.

In addition, the default information of individual entities can often be inferred by random thinning techniques, see Giesecke, Goldberg and Ding (2007)[32] for details.

Similarly, Hurd and Kuznetsov (2006a)[34] and (2006b)[35] induce correlation by a random change in the speed of time.

For a comparative analysis of correlation approaches in finance, see Albanese, Li, Lobachevskiy, and Meissner (2010).