Convertible bonds pricing model

We show at FIGURE 13.10 a basic spreadsheet for a convertible bond pricing model. The model parameters are shown at the top. We also show at Appendix III the cell formulae so that the sheet can be reproduced by... 

As noted, the share price is a key parameter of the option pricing model. An increase in the underlying share price will result in a rise of the convertible price, and a decrease in the share price will result in a fall of the convertible price. Figure 9.9 illustrates the comparison between the convertible bond price and share price of Intel Corporation. 

Therefore, the model is easy to implement and gives similar results as the binomial tree. Because B S works in continuous compounding while the binomial tree in discrete time, the models give the same results only if the binomial tree has a high number of steps. The more periods in binomial tree are implemented, the nearer is the value that we get in both models. Consider the convertible bond pricing shown in Section 9.3.1. In that analysis we estimate the value of a call option using the binomial tree, obtaining a value per call of 0.46. 

As explained in the introduction, the value of a convertible bond is the sum of two main components, the option-free bond and a call option on underlying security. The value of the option-free bond, or bond floor, is determined as the sum of future payments (coupon and principal at maturity). Therefore, the bond component is influenced by three main parameters, that is the maturity, the coupon percentage on par value and the yield to maturity (discount rate). Differently, the value of a call option can be found mainly through two option pricing models, Black Scholes model and binomial tree model. 

The second parameter that affects convertible value is the volatility. In fact, the volatility of the underlying asset is the main element that moves the value of the embedded option, in which pricing models are very sensitive from this parameter. Note that convertible price rises as the volatility increases. The chart shown in Figure 9.11 defines the value of the convertible bond with the volatilities of 25%, 35% and 45%. 

Stock dividends. As exposed in Section 9.4.3, the introduction of dividend payments into the model limits the growth of stock price tree, making the value of the convertible bond lower ... 

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. 

Convertible instruments are usually issued with attached call or put options. Such features can be implemented into the valuation model. If a soft call feature has been implemented, it enables the issuer to force the conversion when the share price overcomes a percentage or trigger level above the conversion price. However, this option cannot be called in the first years hard call . Differently, after the protection period, the issuer can exercise the option. This second time is referred to soft call . Using the same example shown in Section 9.3.1, we assume that the bond may be redeemed in whole but not in part at their principal amount plus accrued interest on the last 2 years, in which the maturity date is at 20 February 2019. On and after this call date , if the share price exceeds 130% of the conversion price the issuer can force the conversion. Figure 9.23 shows the stock price tree in which at years 4 and 5 the stock price is above the threshold. 

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