Theoretical solution versus industry standard: Optimal leverage function for CPDOs

Author： Baydar Evren  

Publisher： Springer Publishing Company

ISSN： 1864-0281

Source： Blätter der DGVFM, Vol.30, Iss.1, 2009-04, pp. : 15-29

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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.

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