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Pricing formulae for constant proportion debt obligation notes: The Laplace transform technique

2014-03-15
Cekic, A. I.
Uğur, Ömür
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. (C) 2013 Elsevier B.V. All rights reserved.