A Non-Zero Sum Game Approach to Convertible Bonds: Tax Benefit, Credit Risk and Late Call

Nan Chen
Department of Systems Engineering & Engineering Management
The Chinese University of Hong Kong


Monday, March 8, 2010
3:00 - 4:00 PM
Terman Engineering Center, Room 453


Abstract:

Convertible bond is a hybrid security which embodies the characteristics of both straight bond and equity. The conflict of interests between bondholders and shareholders affects the security prices significantly. In this paper, we investigate how to use a non-zero-sum game framework to model their interaction and to evaluate the bond accordingly. Mathematically, this problem can be reduced down to a system of variational inequalities. We manage to explicitly derive a unique Nash equilibrium to the game. Our model shows that credit risk and tax benefit can produce considerable impact on the optimal strategies of both parties. The shareholder may issue a call when the debt is out-of-the-money or in-the-money. This is consistent with the empirical findings of "late and early calls" (Ingersoll (1977), Mikkelson (1981), Ederington et al. (1997) and Cowan et al. (2001)). In addition, the optimal call policy under our model offers an explanation to some stylized patterns related to the returns of the company value as well.



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