  In this paper, we develop Stein's method for negative binomial distribution
using call function defined by $f_z(k)=(k-z)^+=\max\{k-z,0\}$, for $k\ge 0$ and
$z \ge 0$. We obtain error bounds between $\mathbb{E}[f_z(\text{N}_{r,p})]$ and
$\mathbb{E}[f_z(V)]$, where $\text{N}_{r,p}$ follows negative binomial
distribution and $V$ is the sum of locally dependent random variables, using
certain conditions on moments. We demonstrate our results through an
interesting application, namely, collateralized debt obligation (CDO), and
compare the bounds with the existing bounds.
