Saddlepoint Approximations for Expectations and an Application to CDO Pricing

We derive two types of saddlepoint approximations for expectations in the form of E[(X - K)+], where X is the sum of n independent random variables and K is a known constant. We establish error convergence rates for both types of approximations in the independently and identically distributed case. The approximations are further extended to cover the case of lattice variables. An application of the saddlepoint approximations to CDO pricing is presented. © 2011 Society for Industrial and Applied Mathematic