Consider two correlated assets $X$ and $Y$ with marginals $f_X$ and $f_Y$ and linear correlation coefficient $\rho$. Assume a Gaussian copula, $C_{X,Y}(x,y,\rho)$, can approximate the joint CDF well enough for this exercise. Value the contingent claim: $g_T=(X-K)1_{X>K}1_{L<Y<U}$. Assume interest rates are zero. Your final answer should be a numerical integral with a copula.

My attempt:

$g_t \\= \int_{k}^{\infty}\int_L^U(x-K)f_{X,Y}(x,y)dydx\\=\int_K^\infty(x-K)(F_{X,Y}(x,U) - F_{X,Y}(x,L))dx\\=\int_K^\infty(x-K)(C_{X,Y}(F_X(x),F_Y(U), \rho) - C_{X,Y}(F_X(x),F_Y(L), \rho))dx$

When I try to value the integral above, I get that it doesn't converge. What am I doing wrong?


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