# Value the claim $(X-K)1_{X>K}1_{L<Y<U}$

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. 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?