Convertible bond pricing models and their applications

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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.