When bond issuers, such as corporations, issue bonds, one of the risks they face is the interest rate risk. When interest rates decrease, bond prices increase. While existing bondholders will find their bonds more valuable, bond issuers, on the other hand, find themselves in a losing position since they will be issuing higher interest payments than the prevailing interest rate. Conversely, when interest rates increase, bond issuers are at an advantage since they are able to continue issuing the same low interest payments as agreed on the bond contract specifications.
To capitalize on interest rate changes, bond issuers may embed options within a bond. This allows the issuer the right, but not the obligation, to buy or sell the issued bond at a predetermined price during a specified period of time. An American type of bond option allows the issuer to exercise the rights of the option at any point of time during the lifetime of a bond. An European type of bond option allows the issuer to exercise the rights of the option at a specific date. The exact style of the date of exercise varies from bond option to bond option. Some issuers may choose to exercise the right of the bond option when the bond has been in circulation in the market for over a year. Some issuers may choose to exercise the bond option at one of several specific dates. Regardless of the exercise dates of the bond, you may price the bond with an embedded option as:
The pricing of a bond with no option is fairly straightforward: the present value of the bond to be received at a future date, including all coupon payments. A number of assumptions are to be made on the theoretical interest rates into the future at which the coupon payments may be reinvested. One such assumption might be the movement of interest rates as implied by short rate models, which we have covered in the preceding section. Another assumption might be the movement of interest rates within a binomial or trinomial tree. For simplicity, in bond pricing studies, we will price zero-coupon bonds that will not issue coupons during the lifetime of the bond.
To price an option, you would have to determine available exercise dates. Starting from the future value of the bond, the bond price is compared against the exercise price of the option and traverses back to the present time using a numerical procedure, such as a binomial tree. This price comparison is performed at time points, where the bond option may be exercised. By the no-arbitrage theory, accounting for the present excess values of the bond when exercised, we obtain the price of the option. For simplicity, in bond pricing studies in the later sections of this chapter, we will treat the embedded option of zero-coupon bonds as an American option.
In an economic condition where there are high interest rates, bond issuers are likely at risk of facing an interest rate decrease and having to continue with issuing higher interest payments than the prevailing interest rate. As such, they may choose to issue callable bonds. The callable bond contains an embedded agreement to redeem the bond at agreed dates. Existing bond holders are considered to have sold a call option to the bond issuer. In the event that the interest rates do fall and the corporation has the rights to exercise the option to buy back the bond during that period at a specific price, they may choose to do so. The company can then issue new bonds at lower interest rates. This also means that the company is able to raise more capital in the form of higher bond prices.
Unlike callable bonds, the owner of puttable bonds has the right, but not the obligation, to sell the bond back to the issuer at an agreed price during a certain period. Owners of puttable bonds are considered to have bought a put option from the bond issuer. When interest rates increase, values of existing bonds become less valuable and puttable bond holders are more incentivized to exercise the right to sell the bond at a higher exercise price. Since puttable bonds are more beneficial to buyers than to the issuers, they are generally less common than callable bonds. Variants of puttable bonds can be found in the form of loan and deposition instruments. A customer who has placed a fixed-rate deposit with a financial institution receives interest payments on specified dates. They are entitled to withdraw the deposit at any time. As such, a fixed-rate deposit instrument can be thought of as a bond with an embedded American put option.
An investor who wishes to borrow money from a bank enters a loan agreement, making interest payments during the lifetime of the agreement until the debt, together with the principal amount and agreed interests, is fully repaid. The bank can be considered as buying a put option on a bond. Under certain circumstances, the bank may exercise the right to redeem the full value of the loan agreement.
Thus, the price of puttable bonds can be thought of as:
Convertible bonds are issued by companies and contain an embedded option that allows the holder to convert the bond into a number of shares of common stock. The amount of shares to be converted for a bond is defined as the conversion ratio, which is determined such that the dollar amount of shares is the same as the value of the bond.
Convertible bonds have similarities with callable bonds. They allow the bond holders to exercise the bond for an equivalent amount of shares at the specified conversion ratio at agreed times. Convertible bonds typically issue lower coupon rates than nonconvertible bonds, to compensate for the additional value of the right to exercise.
When convertible bond holders exercise their rights into stocks, the company's debts are reduced. On the other hand, the company's stocks become more diluted as the number of shares in the circulation increases, and the company's stock price is expected to fall.
As the company's stock price increases, convertible bond prices tend to increase. Conversely, as the company's stock price decreases, convertible bond prices tend to decrease.
Preferred stocks are stocks that have bond-like qualities. Owners of preferred stocks have seniority of claim of dividend payments over common stocks, which are usually negotiated as a fixed percentage of their par value. Although there is no guarantee of dividend payments, all dividends are paid on preferred stock first over common stock. In certain agreements on preferred stocks, dividends that are not paid as agreed may accumulate until they are paid at a later time. These preferred stocks are known as cumulative.
Prices of preferred stocks typically move in tandem with their common stock. They may have voting rights associated with common shareholders. In the event of bankruptcy, preferred stocks have a first lien of its par value upon liquidation.