A collection of codes on Copula estimation and simulation is shown here, where you can find parameter estimation for t-copula, Grouped-t copula, asymmetric copula, etc., another simple recursive routine to estimate by maximum likelihood the correlation matrix and the degrees of freedom for structured t-copula is shared at http://www.mathworks.com/matlabcentral/fileexchange/19751, the authors impose extra structure on the correlation matrix in the estimation process, where the number of variables is large as compared to the number of observations.

The paper "Estimation of Structured t-Copulas" is available at: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1126401, more paper and codes are at the author's homepage: http://www.symmys.com/AttilioMeucci/Home/Home.html
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