Interest payment dates

The Calculation Agent s main role is to determine the EURIBOR rate and calculate and notify all relevant parties of the interest amounts owing to the Noteholders on each Interest Payment Date. The Calculation Agent will be part to the Agency Agreement. 

The Principal Paying Agent is responsible for setting up and monitoring the various cash accounts on behalf of the Issuer. It is also responsible for transferring monies to the Payment Account in readiness for Interest Payment Dates. One of the accounts is the Expense Account, which will have monies on deposit which may be withdrawn to pay for the issuer s Extraordinary Administrative Expenses. 

The monies in the Expense Account will not be drawn until the share capitalization costs of the Issuer (equal to 124,000) are used up to cover such expenses. Thereafter as invoices become due and payable monies will be drawn and on each Interest Payment Date (and to the extent there are sufficient funds), to the extent that the Expense Account balance is below 25,000, monies will be applied from distribution to replenish to 50,000. 

The Senior Notes are also pickable, which means that if fnnds are not available on an Interest Payment Date to pay the full amount of interest owing to the Class A or Class B Notes, such amount will be deferred and therefore not dne and payable on such Interest Payment Date bnt will be ontstanding on the applicable Notes and payable with funds available in fntnre Interest Payment Dates. The ratings by the rating agencies will therefore be based on ultimate payment of principal and interest and not timely payment of the same. 

The Senior Notes shall be redeemed (in whole but not in part) by the Issuer at the direction of the holders of more than 50% of the aggregate principal amount outstanding as at the Final Closing Date of the Junior Notes. Any such redemption is subject to the following conditions (a) no such redemption may occur on any date other than an Interest Payment Date (b) other than as a result of the occurrence of certain tax events, no such redemption may occur prior to the end of the Reinvestment Period and (c) no optional redemption of the Senior Notes may occur unless there are sufficient proceeds to repay all the Senior Notes and any accrued and unpaid fees and expenses. 

On any Interest Payment Date on or after payment in full of the Senior Notes and any accrued fees and expenses, the Junior Notes shall be redeemed (in whole but not in part) by the Issuer at the direction of holders more than 50% of the aggregate principal amount outstanding as at the Final Closing Date of the Junior Notes. 

N = number of interest periods t = each interest payment date ri = the mortgage yield... 

The swap s value will change by approximately the same amount, but in the opposite direction, as the bond s value. The match will not be exact. It is very difficult to establish a precise hedge for a number of reasons, including differences in day count and in maturity, and basis risk. To minimize the mismatch, the swap s maturity should be as close as possible to the bond s. Since swaps are OTC contracts, it should be possible to match interest-payment dates as well as maturity dates. 

At the same time it must be ensured that the steadily increasing number of data can be provided at ever shorter intervals so as to be able to meet the contractual payment dates and avoid interest-related losses. 

We obtain a closed-form solution for the special case of a coupon bond option containing only one payment date (see section 5.3.1). Furthermore, there exists a closed-form solution assuming one-factor interest rate models (see Jamishidian [42]). 

Cash flow is simply the cash that is expected to be received in the future from owning a financial asset. For a fixed-income security, it does not matter whether the cash flow is interest income or repayment of principal. A security s cash flows represent the sum of each period s expected cash flow. Even if we disregard default, the cash flows for some fixed-income securities are simple to forecast accurately. Noncallable benchmark government securities possess this feature since they have known cash flows. For benchmark government securities, the cash flows consist of the coupon interest payments every year up to and including the maturity date and the principal repayment at the maturity date. 

In order to value a bond with the settlement date between coupon payments, we must answer three questions. First, how many days are there until the next coupon payment date From Chapter 1, we know the answer depends on the day count convention for the bond being valued. Second, how should we compute the present value of the cash flows received over the fractional period Third, how much must the buyer compensate the seller for the coupon earned over the fractional period This is accrued interest that we computed in Chapter 1. In the next two sections, we will answer these three questions in order to determine the full price and the clean price of a coupon bond. 

The last step in this process is to find the bond s value without accrued interest (called the clean price or simply price). To do this, the accrued interest must be computed. The first step is to determine the number of days in the accrued interest period (i.e., the number of days between the last coupon payment date and the settlement date) using the appropriate day count convention. For ease of exposition, we will assume in the example that follows that the actual/actual calendar is used. We will also assume there are only two bondholders in a given coupon period— the buyer and the seller. 

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 most obvious source of dollar return is the annual coupon interest payments. For the 1 million par value of this 5-year bond, the annual coupon payments consist of five payments of 30,000 with the first occurring on April 11, 2004. Since this bond has a settlement date that does not fall on a coupon payment date, the buyer pays the seller accrued interest. There are 89 days the first interest accrual date (11 April 2003) and the bond s settlement date of 9 July 2003. In addition, there are 366 days in the annual coupon period. At settlement, the buyer will pay the seller 7,295.08 (per 1 million in par value) in accrued interest which is calculated as follows ... 

For settlement amounts, real accrued interest is calculated as for ordinary OATs. Clean price and accrued are each multiplied by the Index Ratio to arrive at a cash settlement amount. For actual coupons paid, the (real) annual coupon rate is multiplied by the Index Ratio for the payment date, and likewise for the par redemption amount (with the cash value subject to a par floor). 

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. 

Gilts are registered securities. All gilts pay coupon to the registered holder as at a specified record date the record date is seven business days before the coupon payment date. The period between the record date and the coupon date is known as the ex-dividend or ex-div ( xd ) period during the ex-dividend period the bond trades without accrued interest. This is illustrated in Exhibit 9.1. 

To derive the swap term structure, observed market interest rates combined with interpolation techniques are used also, dates are constructed using the applicable business-day convention. Swaps are frequently con-strncted nsing the modified following bnsiness-day convention, where the cash flow occurs on the next business day unless that day falls in a different month. In that case, the cash flow occurs on the immediately preceding business day to keep payment dates in the same month. The swap curve yield calculation convention frequently differs by currency. Exhibit 20.2 lists the different payment frequencies, compounding frequencies, and day count conventions, as applicable to each currency-specific interest rate type. 

The final component of the default swap is the accrued premium that may be payable by the buyer to the seller. If a default occurs somewhere in between two premium payment dates, which is likely considering there are only four payment dates a year on a quarterly default swap, then it is standard market practice for the buyer of protection to pay the accrued premium from the most recent premium payment date to and including the date of default. The value of this accrued on default is calculated in a similar manner to the value of the default protection above. However, instead of receiving 1 - R upon a default, the buyer will be paying a certain amount of accrued interest. 

A bond s term to maturity is crucial because it indicates the period during which the bondholder can expect to receive coupon payments and the number of years before the principal is paid back. The principal of a bond—also referred to as its redemption value, maturity value, par value, or face value—is the amount that the issuer threes to repay the bondholder on the maturity, or redemption, date, when the debt ceases to exist and the issuer redeems the bond. The coupon rate, or nominal rate, is the interest rate that the issuer agrees to pay during the bond s term. The annual interest payment made to bondholders is the bond s coupon. The cash amount of the coupon is the coupon rate multiplied by the principal of the bond. For example, a bond with a coupon rate of 8 percent and a principal of 1,000 will pay an annual cash amount of 80. 

This formula calculates the fair price on a coupon payment date, so there is no accrued incorporated into the price. Accrued interest is an... 

All bonds except zero-coupon bonds accrue interest on a daily basis that is then paid out on the coupon date. As mentioned earlier, the formulas discussed so far calculate bonds prices as of a coupon payment date, so that no accrued interest is incorporated in the price. In all major bond markets, the convention is to quote this so-called clean price. 

Accrued interest compensates sellers for giving up all the next coupon payment even though they will have held their bonds for part of the period since the last coupon payment. A bond s clean price moves with market interest rates. If the market rates are constant during a coupon period, the clean price will be constant as well. In contrast, the dirty price for the same bond will increase steadily as the coupon interest accrues from one coupon payment date until the next ex-dividend date, when it falls by the present value of the amount of the coupon payment. The dirty price at this point is below the clean price, reflecting the fact that accrued interest is now negative. This is because if the bond is traded during the ex-dividend period, the seller, not the buyer, receives the next coupon, and the lower price is the buyer s compensation for this loss. On the coupon date, the accrued interest is zero, so the clean and dirty prices are the same. 

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. 

An interest rate swap is an agreement between two counterparties to make periodic interest payments to one another during the life of the swap. These payments take place on a predetermined set of dates and are based on a notional principal amount. The principal is notional because it is never physically exchanged—hence the off-balance-sheet status of the transaction—but serves merely as a basis for calculating the interest payments. 

Although for the purposes of explaining swap structures both parties are said to pay and receive interest payments, in practice only the net difference between both payments changes hands at the end of each interest period. This makes administration easier and reduces the number of cash flows for each swap. The final payment date falls on the maturity date of the swap. Interest is calculated using equation (7.1). 

Consider a plain vanilla interest rate swap with a notional principal of M that pays n interest payments through its maturity date, T. Payments are made on dates 4 where i = 1,. ..n. The present value today of a future payment made at time r, is denoted as PV 0, t,). If the swap rate is r, the present value of the fixed-leg payments, PVfi s is given by equation (7.2). 

As explained in chapter 3, zero-coupon, or spot, rates are true interest rates for their particular terms to maturity. In zero-coupon swap pricing, a bank views every swap, even the most complex, as a series of cash flows. The zero-coupon rate for the term from the present to a cash flows payment date can be used to derive the present value of the cash flow. The sum of these present values is the value of the swap. 

The conventional yield—the one usually quoted—is almost invariably different from the true yield. This is because the conventional calculation derives the number of interest periods between the value date and the cash flows based on exact half-year intervals between payments, ignoring the delays that occur when the payment dates fall on nonbusiness days. 

Example A Treasury bond with a face value of 100,000 is issued with a coupon rate of 8.75 percent. Coupon payment dates for this bond are November 15 and May 15. If this bond is purchased on January 5, what is the value of accrued interest ... 

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