A Nonzero‐Sum Game Approach to Convertible Bonds: Tax Benefit, Bankruptcy Cost, and Early/Late Calls

37 Pages Posted: 10 Jan 2013

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: January 2013

Abstract

Convertible bonds are hybrid securities that embody the characteristics of both straight bonds and equities. The conflicts of interest between bondholders and shareholders affect the security prices significantly. In this paper, we investigate how to use a nonzero‐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.” In addition, the optimal call policy under our model offers an explanation for certain stylized patterns related to the returns of company assets and stocks on call.

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

Suggested Citation

Chen, Nan and Dai, Min and Wan, Xiangwei, A Nonzero‐Sum Game Approach to Convertible Bonds: Tax Benefit, Bankruptcy Cost, and Early/Late Calls (January 2013). Mathematical Finance, Vol. 23, Issue 1, pp. 57-93, 2013. Available at SSRN: https://ssrn.com/abstract=2198774 or http://dx.doi.org/10.1111/j.1467-9965.2011.00488.x

Nan Chen

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

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
1
Abstract Views
575
PlumX Metrics