Coupon-paying bonds

All bonds coupon-paying bonds accrue interest on a daily basis, and this is then paid out on the coupon date. In determination of the fair price... 

We now have everything in place to value an annual coupon-paying bond. Recall, the present value of an annuity is equal to... 

Real interest is accrued on a European 30/360 basis. To calculate settlement amounts, real accrued interest and clean price are multiplied by the indexation ratio for the settlement date, as for France s issues. Also, as in France, coupon and redemption amounts are calculated by multiplying the real value of the payment by the indexation ratio for the payment date. All five coupon-paying bonds pay on 1 December each year. 

The denominator of this ratio is the number of calendar days between the last coupon date and the next one. This figure depends on the day-count convention (see below) used for that particular bond. Using /, the price formula is modified as (1.17) (for annual-coupon-paying bonds for bonds with semiannual coupons, r/2 replaces r). 

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. 

For settlement purposes there are separate rounding conventions applied to the zero-coupon and coupon-paying issues. For zero-coupon bonds there is no rounding in the calculation, but the settlement price is rounded to the nearest krona. Coupon bonds are rounded once before you get to the settlement price, the clean price is rounded to three decimal places before adding on accrued interest. The settlement price is then rounded to the nearest krona. 

Consider a bond paying a periodic cash payment p at times Ti,T2,...,T , and the principal at maturity T = T j. A coupon bond can be mapped into a portfolio of discount bonds with corresponding maturities (under one source of uncertainty, that is one factor model). The value of a coupon bearing bond at time t [Pg.594]

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-... 

In the case of global notes, acting on behalf of the issuer to supervise payments of interest and principal to investors via the clearing systems, and in the case of definitive notes, paying out interest and coupon on presentation by the investor of the relevant coupon or bond to the Paying Agent. 

A specialised depositary will hold definitive notes representing aggregate investor positions held in a particular issue on coupon and maturity dates it presents the coupons or bond to the paying agent and passes the proceeds on to the clearing system. 

Bonds in the U.S. domestic market—as opposed to international securities denominated in U.S. dollars, such as USD Eurobonds—usually pay semiannual coupons. Such bonds may be priced using the expression in (1.13), which is a modification of (1.12) allowing for twice-yearly discounting. 

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. 

Zero-coupon indexation. Zero-coupon indexed bonds have been issued in Sweden. As their name implies, they pay no coupons the entire inflation adjustment occurs at maturity, applied to their redemption value. 

Current pt. Current-pay bonds have been issued in Turkey. They are similar to interest-indexed bonds in that their redemption payments at maturity are not adjusted for inflation. They differ, however, in their term cash flows. Current-pay bonds pay an inflation-adjusted coupon plus an indexed amount that is related to the principal. In effect, they are inflation-indexed floating-rate notes. 

Reinvestment risk. Like holders of a conventional bond, investors in a coupon indexed bond are exposed to reinvestment risk because they cannot know in advance what rates will be in effect when the bond s coupon payments are made, investors cannot be sure when they purchase their bond what yield they will earn by holding it to maturity. Bonds, such as indexed annuities, that pay more of their return in the form of coupons carry more reinvestment risk. Indexed zero-coupon bonds, like their conventional counterparts, carry none. 

In a conventional sequential-pay structure, the other classes in the CMO receive some of their principal prepayments from the Z bond, which lowers their average-life volatility. Z bonds are an alternative for investors who might otherwise purchase Treasury zero-coupon bonds. Like zero coupons, these bonds have no reinvestment risk, but they have higher yields than Treasury strips with similar average lives. 

Treasury inflation-protected securities (TIPs) are one of the most innovative financial products to appear in recent years. They pay a real coupon, plus the return on the Consumer Price Index (CPI). Thus, they automatically protect investors 100% against rising inflation, a property no other security possesses. Further, in a rising inflation environment, returns on TIPs are negatively correlated with those of bonds and other assets whose prices tend to decline when inflation rises. 

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 continuously compounded gross redemption yield at time ton a default-free zero-coupon bond that pays 1 at maturity date 7 is x. We assume that the movement in X is described by... 

The continuously compounded yield at time t of a risk-free zero-coupon bond paying 1 on maturity at time T is given by ... 

Inflation-Linked Bonds with Zero-Coupon Indexation Zero-coupon bonds linked to the inflation do not pay coupons. Therefore, the unique adjustment is made to the principal. These types of bonds offer no... 

Consider the example in which a hypothetical conventional bond and inflation-linked bond pay an annual coupon of 2%, with a discount rate of 3%. The second one pays coupons and principal linked to the inflation. To understand the effect of the inflation, Figure 6.6 shows the loss of value of a conventional bond compared to an inflation-linked bond. The evidence is that maintaining a flat discount rate, a change of the inflation rate affects only to an inflation-linked bond, increasing its value, while the value of a conventional bond remains unchanged. In reality, over the bond s life, the value of the first one remains unchanged while the value of second one depreciates as the inflation increases. 

Considering the example in which a 5-year bond pays an annual coupon of 1%, with a discount rate of 2%. The bond price is given by the following steps ... 

Asset-swap spread It is determined by combining an interest-rate swap and cash bond. Generally, bonds pay fixed coupons therefore, it will be combined with an interest-rate swap in which the bondholder pays fixed coupons and receives floating coupons. The spread of the floating coupon over an interbank rate is the asset-swap spread. ... 

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). 

A fixed-rate bond pays fixed coupons during the bond s life known with certainty. Conversely, a floating-rate note ox floater pays variable coupons linked to a reference rate. This makes the coupon payments uncertain. The main pim-pose of this debt instrument is to hedge the risk of rising interest rates. Although the financial crisis and liquidity provided by central banks have decreased the level of interest rates, they will at some point of course rise in future years. 

Another way to calculate the yield return is the discounted margin. It differs from the simple margin because the first one amortizes the bond s premium or discount at a constantly compounded rate. The main disadvantage of this method is that it requires estimation of the reference rate over the bond s life. Assuming a bond paying semi-annual coupons, the discounted margin is given by (10.5) ... 

Index duration is usually equal to the time until the next reset date, whereas spread duration is equal to a modified duration of a bond paying fixed coupon, with same coupon payments and time to maturity. Therefore, conventionally floaters have lower index duration and higher spread duration. 

An inverse floating-rate note pays coupons that increase if the reference rate decreases. Therefore, this bond gives a benefit at investors with a negative yield curve. The coupon structure of inverse floaters usually is determined as a fixed interest rate less a variable interest rate linked to a reference index. Moreover, they can include floor provisimis. 

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. 

As noted, the coupon rate is the interest rate the issuer agrees to pay each year. The coupon rate is used to determine the annual coupon payment which can be delivered to the bondholder once per year or in two or more equal installments. As noted, for bonds issued in European bond markets and the Eurobond markets, coupon payments are made annually. Conversely, in the United Kingdom, United States, and Japan, the usual practice is for the issuer to pay the coupon in two semiannual installments. An important exception is structured products (e.g., asset-backed securities) which often deliver cash flows more frequently (e.g., quarterly, monthly). 

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