Convertible bond pricing models and their applications
Project/Area Number  07630021 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Economic statistics

Research Institution  Hitotsubashi University 
Principal Investigator 
KARIYA Takeaki Hitotsubashi University, Institute of Economic Research, Professor, 経済研究所, 教授 (70092624)

CoInvestigator(Kenkyūbuntansha) 
TSUDA Hiroshi NLI Research Institute, Chief Researcher, 金融研究部, 主任研究員

Project Period (FY) 
1995 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1996 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1995 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  Convertible bond / Time Dependent Markov Model / CrossSectional Market Model / BlackScholes formula / Warrant / 一般化最小2乗法 / 銘柄属性 / イールドカプ / イールドカーブ / TDMモデル / CSMモデル / ワラント債 / ブラック=ショールズ公式 / オプション価格 
Research Abstract 
As convertible bond (CB) pricing models, we formulated CBCSM (crosssectional market) model and CBTDM (time dependen Markov) model and verified the empirical validity of these models. These models are naturally stochastic models for market prices. As is well known, a CB carries the attributes of bond and the attributes of potential stock and hence the variations of the price are of complexity associated with these attributes. The former attributes include maturity, coupon rate, default risk, etc.and hence these should be introduced into the models consistently. While, a CB gives the option to convert the bond into stock and hence the price fluctuates with the variations of the potential value of the option. In the CSM model, we value the CB as an exchange option between the value as bond which cannot be directly separated and the value of the convertibility, and assume geometric Brownian motion for the stock price evaluation. In this model, the ex ante attributes of the bond part are incorporated into the model. In the TDM model, in addition, a Markov time series structure is introduced into the CSM model to take into account ex post attributes. In empirical analysis, we use attheendofmonth data for the period 1989.41996.3. First we estimate the CSM model and the residuals of each month are use to estimate the TDM model. In the evaluation of the value of the convertibility, we take into account the correlations of stock prices and apply a Monte Carlo simulation to the evaluation. The performance of the TDM model is quite good compare to the models proposed so far. In fact, in almost all months, the standard errors are less than 2 yen though the number of unknown parameter is 6 with sample sizes 40150. This will be the evidence of the validity of the model.

Report
(3results)
Research Output
(5results)