Convertible bond pricing models and their applications

可转换债券定价模型及其应用

基本信息

批准号：
07630021
负责人：
KARIYA Takeaki
金额：
$ 0.77万
依托单位：
Hitotsubashi University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1995
资助国家：
日本
起止时间：
1995 至 1996
项目状态：
已结题

项目摘要

As convertible bond (CB) pricing models, we formulated CB-CSM (cross-sectional market) model and CB-TDM (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 at-the-end-of-month data for the period 1989.4-1996.3. 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 40-150. This will be the evidence of the validity of the model.

作为可转换键（CB）定价模型，我们制定了CB-CSM（横截面市场）模型和CB-TDM（时间依赖Markov）模型，并验证了这些模型的经验有效性。这些模型是市场价格的自然随机模型。众所周知，CB具有债券的属性和潜在库存的属性，因此价格的变化与这些属性相关。前者属性包括成熟度，息票利率，默认风险等。因此，这些属性应始终如一地引入模型。同时，CB可以选择将债券转换为股票，因此价格随期权的潜在价值的变化而波动。在CSM模型中，我们将CB视为无法直接分开的债券的值和可转换性值之间的交换选项，并在股票价格评估中假设几何布朗尼运动。在此模型中，将键部分的前属性纳入了模型。此外，在TDM模型中，Markov时间序列结构被引入CSM模型以考虑到事后属性。在经验分析中，我们使用1989.4-1996.3时期的月底数据。首先，我们估计CSM模型，每个月的残差用于估计TDM模型。在评估可转换性的价值时，我们考虑了股票价格的相关性，并将蒙特卡洛模拟应用于评估。与迄今为止提出的模型相比，TDM模型的性能非常好。实际上，在几乎所有月份中，标准误差小于2日元，尽管未知参数的数量为6，样本量为40-150。这将是模型有效性的证据。