LAUSR

Let V be a sums of independent nonnegative integer-valued random variables and $$h_z$$ h z be a call function defined by $$h_{z}(v)=(v-z)^+$$ h z ( v ) = ( v - z ) + for $$v\ge 0, z \ge 0$$ v ≥ 0 , z ≥ 0 where $$(v-z)^+=\max \{v-z,0\}$$ ( v - z ) + = max { v - z , 0 } . In this paper, we give bounds of Poisson approximation for $${E}[h_{z}(V)]$$ E [ h z ( V ) ] . These bounds improve the results of Jiao and Karoui (Finance Stoch 13(2):151–180, 2009 ). The technique used is Stein–Chen method with the zero bias transformation. One example of applications for a call function in finance is the standard collateralized debt obligation (CDO) tranche pricing. The CDO is a security backed by a diversified pool of debt obligation such as bounds, loans and credit default swaps.