Pricing Convertible Bonds with Game Theory under Stochastic Interest Rate

• Main Authors: Lu, Te-Ta, 路德大
• Other Authors: Dai, Tian-Shyr
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/20810797020263661963

碩士 === 國立交通大學 === 財務金融研究所 === 101 === This thesis builds a three-dimensional tree that simulates the evolution of the issuing firm value and the stochastic short rate based on the Hull-White short rate tree model to price convertible bonds (CBs). My pricing model considers the influence of the dividend payout, tax benefit and the bankruptcy cost. The game theory is applied to model the sequential conversion behavior under two call policies, minimization of CB value and the maximization of the equity value, and three different conversion scenarios: monopoly case (CBs are owned by one holder), block case (sequential conversion is not allowed), and the competitive case (CBs are owned by many holders and each holder is a price taker). The Nash equilibrium for each node of our tree can be numerically searched to determine the call policy of issuer and the conversion policy of CB holder(s) at that node. I also consider how seniority of CBs influences the prices and the durations of CBs and other outstanding bonds. This thesis also uses the dynamic programming method to estimate the expected maturity of a CB under different scenario. Numerical results suggest that the expected maturity under the maximization of equity policy is larger than the expected maturity under the minimization of CB value policy. This could explain why empirical studies find the ``call delay’’ phenomenon since their researches are based on the latter policy. Besides, the numerical results generated by my model are consistent to the phenomenon found in many empirical studies. For example, I analyze the relationship between the interest rate volatility and the bond price, the relationship between bond duration and the conversion fraction. Finally, I use my model to price the CB issued by NVIDIA in 2000 to confirm the reliability of my model.