Theoretical Solution versus Industry Standard: Optimal leverage function for CPDOs

by Evren Baydar of the University of Kaiserslautern,
Giuseppe Di-Graziano of King’s College London & Deutsche Bank AG, and
Ralf Korn of the University of Kaiserslautern

April 2009

Abstract: In this paper, we derive an optimal leverage function for Constant Proportion Debt Obligations (CPDOs) by using stochastic control techniques. The investor’s goal is to maximise redemption of capital at maturity. The control variable of the problem is the leverage process, i.e. the time dependent notional exposure to the underlying risky index/portfolio.

The control problem is solved explicitly with the help of the Legendre transform applied to the HJB equation of stochastic control. A closed form solution is given for the optimal leverage. Contrary to the industry practise, the optimal leverage derived in this paper is a non-linear, bell-shaped function of the CPDO assets value.

Keywords: CPDO, Constant Proportion Debt Obligation, Optimal Control, Credit Derivatives.

Published in: Blätter der DGVFM, Vol. 30, No. 1, (April 2009), pp. 15-29.

Previously titled: Optimal Leverage Function for CPDOs --and before that-- Optimal leverage in CPDOs

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Related reading: First Generation CPDO: Case Study on Performance and Ratings

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