Perturbed Gaussian copula: introducing the skew effect in co-dependence

Gaussian copula models are often used in the industry when single-asset information is quoted but little is known about their joint relation. These models may arise from correlated stochastic Brownian processes with deterministic volatility and correlation. If stochastic volatility is introduced, skewness and fat tails can be included in the co-dependence but analytic tractability is lost. Alberto Elices and Jean-Pierre Fouque show how this analytic tractability is preserved through another copula derived from an asymptotic expansion of the correlated processes with stochastic volatility around the Gaussian copula case

Copula models arise in the market when quoted information about the behaviour of single assets is available but very little is known about their joint relations. Information about the joint distribution of assets is captured in the prices of basket products written on them. However, as a lot of information is embedded in a single price, some assumptions have to be made about the form of the distribution in order to extract it.

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