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

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.


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Pricing and hedging of constant proportion debt obligations
İşcanoğlu Çekiç, Ayşegül; Uğur, Ömür; Korn, Ralf; Department of Financial Mathematics (2011)
A Constant Proportion Debt Obligation is a credit derivative which has been introduced to generate a surplus return over a riskless market return. The surplus payments should be obtained by synthetically investing in a risky asset (such as a credit index) and using a linear leverage strategy which is capped for bounding the risk. In this thesis, we investigate two approaches for investigation of constant proportion debt obligations. First, we search for an optimal leverage strategy which minimises the mean-...
Citation Formats
A. I. Cekic and Ö. Uğur, “Pricing formulae for constant proportion debt obligation notes: The Laplace transform technique,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 362–370, 2014, Accessed: 00, 2020. [Online]. Available: