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.
Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html