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


Cekic A. I. , UĞUR Ö.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.259, pp.362-370, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 259
  • Publication Date: 2014
  • Doi Number: 10.1016/j.cam.2013.06.006
  • Title of Journal : JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Page Numbers: pp.362-370

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. (C) 2013 Elsevier B.V. All rights reserved.