The Hüsler--Reiss copula (Joe, 2014, p. 176) is
$$\mathbf{C}_{\Theta}(u,v) = \mathbf{HR}(u,v) = \mathrm{exp}\bigr[-x \Phi(X) - y\Phi(Y)\bigr]\mbox{,}$$
where \(\Theta \ge 0\), \(x = - \log(u)\), \(y = - \log(v)\), \(\Phi(.)\) is the cumulative distribution function of the standard normal distribution, \(X\) and \(Y\) are defined as:
$$X = \frac{1}{\Theta} + \frac{\Theta}{2} \log(x/y)\mbox{\ and\ } Y = \frac{1}{\Theta} + \frac{\Theta}{2} \log(y/x)\mbox{.}$$
As \(\Theta \rightarrow 0^{+}\), the copula limits to independence (\(\mathbf{\Pi}\); P). The copula here is a bivariate extreme value copula (\(BEV\)), and the parameter \(\Theta\) requires numerical methods.