Fair Value of a Convertible Bond The Binomial Model

Fair Value of a Convertible Bond The Binomial Model 

The fair price of a convertible bond is the one that provides no opportunity for arbitrage profit that is, it precludes a trading strategy of running simultaneous but opposite positions in the convertible and the underlying equity in order to realize a profit. Under this approach we consider now an application of the binomial model to value a convertible security. Following the usual conditions of an option pricing model such as Black-Scholes (1973) or Cox-Ross-Rubinstein (1979), we assume no dividend payments, no transaction costs, a risk-free interest rate, and no bid-offer spreads. 

Application of the binomial model requires a binomial tree detailing the price outcomes from the start period, which is shown at FIGURE 13.3. In the case of a convertible bond this will refer to the prices for the underlying asset, which is the ordinary share of the issuing company. 

If we accept that the price of the equity follows such a path, we assume that it follows a multiplicative binomial process. This is a geometric 

The value of a convertible bond is a function of a number of variables. For the purposes of this analysis we set parameters required as follows  

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