Convertible bond pricing models and their applications

作为可转债的定价模型，我们分别建立了CB- csm（横截面市场）模型和CB- tdm（时间相关马尔可夫）模型，并验证了模型的实证有效性。这些模型自然是市场价格的随机模型。众所周知，转债具有债券的属性和潜在股票的属性，因此价格的变化与这些属性有关。前一种属性包括期限、票面利率、违约风险等，因此这些属性应该一致地引入模型中。然而，转债提供了将债券转换为股票的期权，因此价格随期权潜在价值的变化而波动。在CSM模型中，我们将转债视为不可直接分离的债券价值与可兑换性价值之间的交换期权，并假设股票价格的几何布朗运动。在该模型中，将bond部件的先验属性纳入到模型中。此外，在TDM模型中，在CSM模型中引入了马尔可夫时间序列结构，以考虑事后属性。在实证分析中，我们使用1989.4-1996.3期间的月末数据。首先对CSM模型进行估计，然后利用每个月的残差对TDM模型进行估计。在可兑换性价值的评估中，我们考虑了股票价格的相关性，并应用蒙特卡罗模拟进行了评估。与目前提出的模型相比，TDM模型的性能相当好。事实上，在几乎所有月份，尽管未知参数的数量为6个，样本量为40-150个，但标准误差都小于2日元。这将是模型有效性的证据。

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.