When an investor purchases non-callable or non-putable convertible bonds, he would be buying a non-callable/non-putable straight security and also buying a call option on the stock, where the number of shares that can be purchased with the call option is equal to the conversion ratio. Therefore, we need to determine the fair value of the call option to determine the value of the convertible bond. The value of the convertible bond is as follows:
We have to add the value of the option to the straight value because the investor purchases a call option on the stock. To get the value of a convertible bond, the value of call option on the bond is to be deducted from the value of convertible security. Therefore, the value is equal to:
The value of the issuer's right to call depends on two factors: (i) future interest rate volatility, and (ii) economic factors that determine whether or not it is optimal for the issuer to call the security. If the callable convertible bond also has putable option, then the formula to determine the value is:
Black-Scholes option pricing model is generally used to determine the theoretical value of a call option. However, in situations where multiple options involving options that depend on future interest rates are considered, Black-Scholes method cannot be used. Researchers have suggested various models for valuation which can be classified under one-factor model or multi-factor models. But, the most common model is the one-factor model based on the price movement of the underlying common stock.