How can you calculate Spearman's rho of the comonotinicity copula?
Comonotonicity Copula: $Cm(u1, u2) = min(u1, u2)$
Spearmans rho: $\rho = 12 \int_{0}^{1}\int_{0}^{1} C(u1,u2) du1 du2 -3$
Obviously, this results in the following: $12 \int_{0}^{1}\int_{0}^{1} min(u1, u2) du1 du2 -3$
But how can I solve this integral with a minimum?
I solved it myself with the help of the following post:
user21436, integrals involving minimum function, URL (version: 2012-02-05): https://math.stackexchange.com/q/105854
$$\begin{align*}\int_o^t\int_0^t \min\{x,y\} \mathrm dy ~~\mathrm dx&=\dfrac{t^3}{3}\end{align*}$$
$$12 \int_{0}^{1}\int_{0}^{1} min\{u1, u2\} du1 du2 -3 = 12 * 1^3/3 -3 = 1$$