There isn't a direct toolbox which directs you for the estimation for Egarch - EVT - COPULA Model. But there are some toolboxes which can direct you for your requirements.
Econometrics Toolbox: For GARCH/EGARCH modeling.
- https://in.mathworks.com/help/econ/egarch-model.html
- https://in.mathworks.com/help/econ/specify-egarch-models-using-egarch.html
Statistics and Machine Learning Toolbox: For copula distributions and correlated samples
MathWorks provides an example on “Using Extreme Value Theory and Copulas to Evaluate Market Risk”, which uses a Student’s t copula and Extreme Value Theory (EVT) in a Monte Carlo simulation technique.
User-written Code: For more specific implementations, you may need to write custom functions or find user-contributed code on platforms like MATLAB Central File Exchange.
I hope this helps.