Convertible bonds embedded option

In this chapter we present a discussion on convertible bonds, which have become popular hybrid financial instruments. Convertible bonds are financial instmments that give the bondholders the right, without imposing an obligation, to convert the bond into underlying security, usually common stocks, under conditions illustrate in the indenture at the time of issue. The hybrid characteristic defines the traditional valuation approach as the sum of two components the option-free bond and an embedded option (call option). The option element makes the valuation not easy, above all in pricing term sheets with specific contract clauses as the inclusion of soft calls, put options and reset features. The chapter shows practical examples of valuation in which financial advisors and investment banks adopts in different contexts. 

The embedded option component in convertible bonds makes the valuation sensitive from three main parameters share price, volatility and interest rate. These parameters affect the value of a convertible bond for both situations ... 

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%. 

The put option gives at the bondholder the right, but not the obligation to redeem the convertible bond to the issuer at the price defined in the indenture, hi this case, the value of the convertible bond is greater (the yield is lower) than the one without embedded put option. Usually, the issuer is required to redeem the convertible bond for cash, shares or both elements. 

Conversely, at the lowest node, the hedge ratio is 0 because the option is out of money or 0. This means that in the first case the bond trade like the equity, while in the second case like a conventional bond. Therefore when the share price increases the delta approaches unity, implying that the option is deeply in the money. In contrast, when the share price is low relative to the conversion price, the sensitivity of the convertible and therefore of the embedded option is low. 

The option element in a convertible cannot be stripped out of the bond element, and so is termed an embedded option. The valuation of the bond takes into account this embedded optionality. Note also that unlike a straight equity option, there is no additional payment to make on conversion the holder simply exchanges the bond for the specified number of shares. One could view the price paid for exercising the option as being the loss of the bond element, which is the regular coupon and redemption proceeds on maturity, but this should be viewed as more of an opportunity cost rather than a payment. This bond element is often referred to as the bond floor, which is the straight debt element of the convertible. The bond floor can be viewed as the level at which a vanilla bond issued by the same company would trade, that is, its yield and price. It generally accounts for between 50 percent and 80 percent of the total value. 

We then take the analysis further for a convertible bond plus its embedded option. FIGURE 13.8 shows the price tree for the conventional bond where the share price and conversion price is equal to 100 in the current time period. Note how the conventional bond element of the convertible provides a floor for its price in later periods. 

The convertible price accounts for both the conventional bond element and the embedded option element. If we assume the share price in period t< is 97.01, then in period 6o the share can assume only one of two possible values, 106.25 or 92.24 (see Figure 13.6). In these cases, the value of the call option Ch and Cl will be equal to the higher of the bonds conversion value or its redemption value, which is 106.25 if there is a rise in the price of the underlying or 102.50 if there is a fall in the price of the underlying. This is the range of possible final values for the bond however, we require the current (present) value, so we discount this at the appropriate rate. 

---