A. İ. Çekiç and Ö. Uğur, Pricing Formulae for Constant Proportion Debt Obligation Notes: the Laplace Transform Technique, Journal of Computational and Applied Mathematics, 259(B), pp. 362-370, (March 2014).

### Abstract

In this paper we derive closed form pricing formulae for the constant proportion debt obligation (CPDO) by using the Laplace transform technique. First, we present the pricing equation as a combination of a pricing problem (conditional expectation) and a static part that depends only on time. Then, we indicate that the pricing problem is in fact a pricing of a barrier option written on the shortfall. Hence, we derive explicit solutions of such barrier option problems when the shortfall follows either a diffusion or a double exponential jump diffusion process. Finally, we illustrate and discuss the results using numerical applications.

*Keywords*: Constant Proportional Debt Obligation, Laplace Transform, Double Exponential Jump Diffusion Process