A Non-Zero-Sum Game Approach for Convertible Bonds: Tax Benefits, Bankrupt Cost and Early/Late Call

45 Pages Posted: 26 Nov 2010

See all articles by Nan Chen

Nan Chen

The Chinese University of Hong Kong (CUHK)

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management

Date Written: May 25, 2010

Abstract

Convertible bonds are hybrid securities that embody the characteristics of both straight bonds and equities. 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 the interaction between bondholders and shareholders and to evaluate the bond accordingly. Mathematically, this problem can be reduced to a system of variational inequalities and we explicitly derive the Nash equilibrium to the game. Our model shows that credit risk and tax benefit have considerable impacts on the optimal strategies of both parties. The shareholder may issue a call when the debt is in-the-money or out-of-the-money. This is consistent with the empirical findings of “late and early calls” (Ingersoll (1977), Mikkelson (1981), Cowan et al. (1993) and Asquith (1995)). In addition, the optimal call policy under our model offers an explanation for certain stylized patterns related to the returns of company assets and stock on calls.

Keywords: convertible bonds, stochastic non-zero-sum game, Nash equilibrium, tax benefit, credit risk, late and early calls, variational inequalities

JEL Classification: G32, C72, C73

Suggested Citation

Chen, Nan and Dai, Min and Wan, Xiangwei, A Non-Zero-Sum Game Approach for Convertible Bonds: Tax Benefits, Bankrupt Cost and Early/Late Call (May 25, 2010). Available at SSRN: https://ssrn.com/abstract=1714831 or http://dx.doi.org/10.2139/ssrn.1714831

Nan Chen (Contact Author)

The Chinese University of Hong Kong (CUHK) ( email )

Shatin, N.T.
Hong Kong
Hong Kong

HOME PAGE: http://www.se.cuhk.edu.hk/people/nchen.html

Min Dai

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Xiangwei Wan

Shanghai Jiao Tong University - Antai College of Economics & Management ( email )

No.1954 Huashan Road
Shanghai Jiao Tong University
Shanghai, Shanghai 200030
China
+86-21-52301570 (Phone)

HOME PAGE: http://sites.google.com/view/wanxiangwei/research

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