Poisson approximation for call function via Stein-Chen’s method

Abstract

A call function is a nonnegative real-valued function defined by hz(v) = (v−z)+ for z " 0 where (v − z)+ = max{v − z, 0}. There are many applications of call function in finance. For example, the standard collateralized debt obligation tranche pricing. In this work, we give bounds of Poisson approximation for hz(V ) where V is a sum of independent nonnegative integer-valued random variables. The technique used is Stein-Chen’s method with the zero bias transformation. Moreover, in case that V is a sum of independent Bernoulli random variables, we improve the bounds of Poisson approximation for hz(V ) by adding some correction terms.