Fixed coupon bonds

The asset swap is an agreement that allows investors to exchange or swap future cash flows generated by an asset, usually fixed rates to floating rates. It is essentially a combination of a fixed coupon bond and an IRS. We define it thus ... 

An asset swap is a synthetically created structure combining a fixed coupon bond with a fixed-floating IRS, which then transforms the bond s swap fixed rate payments to floating rate. The investor retains the original credit exposure to the fixed... 

Phoa (1998) presents an approximation of the convexity bias as follows. Consider a conventional fixed coupon bond, which has a yield at a future time t of r and a price at this time of P r). The convexity bias is estimated using... 

Although the introduction of the euro has helped to homogenise the characteristics and maturities of the bonds issued, there are still some differences between these countries supplied assets. Euro-denominated fixed coupon bonds bear the brunt of these countries issuance, but there are also some other types of bonds being issued by these countries. 

Note that the swap PVBP, 425, is lower than that of the 5-year fixed-coupon bond, which is 488.45. This is because the floating-rate bond PVBP reduces the risk exposure of the swap as a whole by 63.45. As a rough rule of thumb, the PVBP of a swap is approximately the same as that of a fixed-rate bond whose term runs from the swaps next coupon reset date through the swap s termination date. Thus, a 10-year swap making semiannual payments has a PVBP close to that of a 9.5-year fixed-rate bond, and a swap with 5.5 years to maturity has a PVBP similar to that of a 5-year bond. 

For purposes of analysis, this IDN can be regarded as a fixed-coupon bond plus the double indexation of an interest rate differential. Indexation here refers to a reference rate based on an index. The double indexation creates two long positions in a 5-year dollar-denominated fixed-rate note and two short positions in a euro-denominated fixed-rate note. The short positions remove the euro exchange-rate risk, so investors are exposed only to the euro interest rate risk, which is the desired exposure. 

As already noted, the exact term of a mortgage-backed bond cannot be stated with assurance at the time of issue, because of the uncertainty connected with the speed of mortgage prepayments. As a result, it is not possible to analyze these bonds using the same methods as for fixed-coupon bonds. The most common approach is to assume a fixed prepayment rate—recognizing that, in reality, it will fluctuate with changes in mortgage rates and the economic cycle—and use this to project the bond s cash flows and thus its life span. The prepayment rate selected obviously is very important. This section considers some of the ways the rate is arrived at. 

In this thesis we derived new methods for the pricing of fixed income derivatives, especially for zero-coupon bond options (caps/floor) and coupon bond options (swaptions). These options are the most widely traded interest rate derivatives. In general caps/floors can be seen as a portfolio of zero-coupon bond options, whereas a swaption effectively equals an option on a coupon bond (see chapter (2)). The market of these LIBOR-based interest rate derivatives is tremendous (more than 10 trillion USD in notional value) and therefore accurate and efficient pricing methods are of enormous practical importance. 

To obtain the price of an inflation-linked bond, it is necessary to determine the value of coupon payments and principal repayment. Inflation-linked bonds can be structured with a different cash flow indexation. As noted above, duration, tax treatment and reinvestment risk, are the main factors that affect the instrument design. For instance, index-aimuity bmids that give to the investor a fixed annuity payment and a variable element to compensate the inflation have the shortest duration and the highest reinvestment risk of aU inflation-linked bonds. Conversely, inflation-linked zero-coupon bonds have the highest duration of all inflation-linked bonds and do not have reinvestment risk. In addition, also the tax treatment affects the cash flow structure. In some bond markets, the inflation adjustment on the principal is treated as current income for tax purpose, while in other markets it is not. 

Sundaresan, S., 2009. Fixed Income Markets and Their Derivates, third ed. Elsevier, Burlington. Waggoner, D., 1997. Spline methods for extracting interest rate curves from coupon bond prices. 

Dhillon, U., Lasser, D., 1998. Term premium estimates from zero-coupon bonds new evidence on the expectations hypothesis. J. Fixed Income 8, 52-58. 

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. ... 

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 approach is to compare the floating-rate note with a derived yield of a fixed-rate bond by using an interest rate swap curve matched with floater coupons. Figure 10.4 shows the Bloomberg YASN screen for Mediobanca float... 

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. 

When an option-free bond is issued, the coupon rate and the term to maturity are fixed. Consequently, as yields change in the market, bond prices will move in the opposite direction, as we will see in the next two scenarios. Generally, a bond s coupon rate at the time of issuance is set at approximately the required yield demanded by the market for comparable bonds. By comparison, we mean bonds that have the same maturity and the same risk exposure. The price of an option-free coupon bond at issuance will then be approximately equal to its par value. In the example presented above, when the required yield is equal to the coupon rate, the bond s price is its par value ( 100). 

The price is less than par value and the bond is said to be trading at a discount. This will occur when the fixed coupon rate a bond offers (6%) is less than the required yield demanded by the market (the 7% discount rate). A discount bond has an inferior coupon rate relative to new comparable bonds being issued at par so its price must drop so as to bid up to the required yield of 7%. If the discount bond is held to maturity, the investor will experience a capital gain that just offsets the lower the current coupon rate so that it appears equally attractive to new comparable bonds issued at par. ... 

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. 

The source of dollar return called reinvestment income represents the interest earned from reinvesting the bond s interim cash flows (interest and/or principal payments) until the bond is removed from the investor s portfolio. With the exception of zero-coupon bonds, fixed income securities deliver coupon payments that can be reinvested. Moreover, amortizing securities (e.g., mortgage-backed and asset-backed securities) make periodic principal repayments which can also be invested. 

Without getting into too much detail, these bonds pay a smaller fixed coupon (between 2% and 4%) to which the accumulated inflation in that period is added. By mid-2003 the French Tresor had already issued five different inflation-linked OATs, three of them referenced to French inflation and two of them linked to Eurozone retail prices. The success of these bonds has recently permitted their launch via normal auctions, rather than syndicate issues. As of July 2003, they represent more than 10% of the French bond annual supply. 

The gilts market is primarily a plain vanilla market, and the majority of gilt issues are conventional fixed interest bonds. Conventional gilts have a fixed coupon and maturity date. By volume they made up 82% of the market in June 2002. Coupon is paid on a semi-annual basis. The coupon rate is set in line with market interest rates at the time of issue, so the range of coupons in existence reflects the fluctuations in market interest rates. Unlike many government and corporate bond markets, gilts can be traded in the smallest unit of currency and sometimes nominal amounts change hands in amounts quoted down to one penny ( 0.01) nominal size. 

Bundesobligationen are 5-year, fixed coupon German government bonds with a bullet maturity. 

To buy this bond the investor would pay 105.3% of par value. The investor would receive the fixed coupons of 5.5% of par value. Let us assume that the swap rate is 5%. If the investor in this bond enters into an asset swap with a bank in which the investor pays the fixed coupon and receives LIBOR +/- spread. 

Bonds are debt instruments that represent cash flows payable during a specified time period. They are essentially loans. The cash flows they represent are the interest payments on the loan and the loan redemption. Unlike commercial bank loans, however, bonds are tradable in a secondary market. Bonds are commonly referred to 3S fixed-income instruments. This term goes back to a time when bonds paid fixed coupons each year. That is... 

As discussed in chapter 1, there are two types of fixed-income securities zero-coupon bonds, also known as discount bonds or strips, and coupon bonds. A zero-coupon bond makes a single payment on its maturity date, while a coupon bond makes interest payments at regular dates up to and including its maturity date. A coupon bond may be regarded as a set of strips, with the payment on each coupon date and at maturity being equivalent to a zeto-coupon bond maturing on that date. This equivalence is not purely academic. Before the advent of the formal market in U.S. Treasury strips, a number of investment banks traded the cash flows of Treasury securities as separate zero-coupon securities. 

A zero-coupon bond is the simplest fixed-income security. It makes no coupon payments during its lifetime. Instead, it is a discount instrument, issued at a price that is below the face, or principal, amount. The rate earned on a zero-coupon bond is also referred to as the spot interest rate. The notation P t, T) denotes the price at time r of a discount bond that matures at time T, where T >t - The bond s term to maturity, T - t, is... 

Up to now, the discussion has centered essentially on plain vanilla securities, bonds with a fixed-coupon and maturity date. However, much of the fixed-income markets revolves around more complex instruments, arranged to meet specific investor requirements. These include ... 

Like convertible bonds, synthetic convertible notes provide investors with fixed coupons plus the possibility of profiting from the performance of the reference index. Unlike the ordinary convertible, however, the synthetic pays in cash rather than in shares of the associated equity. 

It was suggested earlier that a swap be seen as a bundle of cash flows arising from the sale and purchase of two cash-market instruments a fixed-rate bond with a coupon equal to the swap rate and a floating-rate bond with the same maturity and paying the same rate as the floating leg of the swap. Considering a swap in this way, equation (7.23) can be rewritten as (7.24). 

Convertible bonds are typically fixed-coupon securities that are issued with an option to be converted into the equity of the issuing company under specified terms and conditions. They have been issued as both senior and subordinated securities. The investors view on the performance of the issuing company s shares is a major factor, because investors are buying into... 

For an investor, holding convertible bonds provides an ability to participate in the fortunes of the company without having to have a direct equity holding. The bondholder has a fixed coupon income stream, together with... 

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