Coupon-paying bonds options

For an underlying coupon-paying bond, the equation must be modified by reducing P by the present value of all coupons paid during the life of the option. This reflects the fact that prices of call options on couponpaying bonds are often lower than those of similar options on zero-coupon bonds because the coupon payments make holding the bonds themselves more attractive than holding options on them. 

We shall repeat the calculation of the coupon-bond call option when the CIR model is employed for the short rates. The procedure is the same as in the case discussed above for the Vasicek model. First we calculate the interest rate such that the present value at the maturity of the option of all later cash flows on the bond equals the strike price. This value is here rjf = 25.05%. Next, we map the strike price into a series of strike prices via equation (18.50) that are then associated with coupon pay-... 

Credit-linked notes are hybrid securities, generally issued by an investment-grade entity, that combine a credit derivative with a vanilla bond. Like a vanilla bond, a standard CLN has a fixed maturity structure and pays regular coupons. Unlike bonds, all CLNs, standard or not, link then-returns to an underlying asset s credit-related performance, as well as to the performance of the issuing entity. The issuer, for instance, is usually permitted to decrease the principal amount if a credit event occurs. Say a credit card issuer wants to fond its credit card loan portfolio by issuing debt. To reduce its credit risk, it floats a 2-year credit-linked note. The note has a face value of 100 and pays a coupon of 7.50 percent, which is 200 basis points above the 2-year benchmark. If more than 10 percent of its cardholders are delinquent in making payments, however, the note s redemption payment will be reduced to 85 for every 100 of face value. The credit card issuer has in effect purchased a credit option that lowers its liability should it suffer a specified credit event—in this case, an above-expected incidence of bad debts. 

Now, we directly see that a swaption in general can be seen as an option on a coupon bond with strike K =1 and exercise date Tq paying the coupons q at the payment dates Ti = Ti. ..Tu. Armed with this, we obtain the price of a receiver swaption... 

The main reason for a borrower to issue cmivertibles is the lower cost of financing than other financial instruments. In fact, the implied equity option feature allows the issuer to pay lower market coupons than a cmiventional bond. This is because the right of cmiversion is hold by the bondholder. In a different case, for instance with a callable issue, the coupons will be greater than a convertible... 

Craisider a hypothetical situation. Assume that an option-free bond paying a semi-annual coupon 5.5% on par value, with a maturity of 5 years and discount rate of 8.04% (EUR 5-year swap rate of 1.04% plus credit spread of 700 basis points). Therefore, the valuation of a conventional bond is performed as follows (Figure 9.4). 

Consider the following example. We assume to have two hypothetical bonds, a treasury bond and a callable bond. Both bonds have the same maturity of 5 years and pay semiannual coupons, respectively, of 2.4% and 5.5%. We perform a valuation in which we assume a credit spread of 300 basis points and an OAS spread of 400 basis points above the yield curve. Table 11.1 illustrates the prices of a treasury bond, conventional bond and callable bond. In particular, considering only the credit spread we find the price of a conventional bond or option-free bond. Its price is 106.81. To pricing a callable bond, we add the OAS spread over the risk-free yield curve. The price of this last bond is 99.02. We can now see that the OAS spread underlines the embedded call option of the callable bond. It is equal to 106.81-99.02, or 7.79. In Section 11.2.3, we will explain the pricing of a callable bond with the OAS methodology adopting a binomial tree. 

Thus far our coverage of valuation has been on fixed-rate coupon bonds. In this section we look at how to value credit-risky floaters. We begin our valuation discussion with the simplest possible case—a default risk-free floater with no embedded options. Suppose the floater pays cash flows quarterly and the coupon formula is 3-month LIBOR flat (i.e., the quoted margin is zero). The coupon reset and payment dates are assumed to coincide. Under these idealized circumstances, the floater s price will always equal par on the coupon reset dates. This result holds because the floater s new coupon rate is always reset to reflect the current market rate (e.g., 3-month LIBOR). Accordingly, on each coupon reset date, any change in interest rates (via the reference rate) is also reflected in the size of the floater s coupon payment. 

Swaptions are options that allow the buyer to obtain at a future time one position in a swap contract. It is quite elementary that an interest rate swap, fixed for floating, can be understood as a portfolio of bonds.To consider this assume that the notional principal is 1. Then the claim on the fixed payments is the same as a bond paying coupons with the rate p and no principal. Let X be the time when the swap is conceived. The claim on the fixed income stream is worth, at time X,... 

Consider two portfolios, Y and Z. Y consists of a call option with a maturity date T and a zero-coupon bond that pays out Xon T Z consists of a put option also maturing on date T and one unit of the underlying asset. The values of portfolios Y and Z on the expiry date are given by equations (8.24) and (8.25), respectively. 

---