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FinPricing provides probably the most comprehensive valuation models for financial products, including computation of:
Bonds are secured loans that investors make to corporations and governments. Corporations and governments issue bonds when they want to raise capital. Bonds typically pay out a stream of cash-flows (the coupon payments) to the bearer, including repayment of the face value at maturity.
Bonds are traded and quoted based on either yield to maturity (YTM), clean price, discounted yield, or discounted margin. The actual settlement clean price depends on the number of coupons available. For bonds with a single remaining coupon, the bond trades at a pure discount (i.e., like a money market instrument). For bonds with multiple remaining coupons, these are priced with a special formula.
From calculation perspective, there are more than 1,500 different types of bonds. The differences are specified by calculation type. Each calc type defines a method used to determine the accrued interest, price, yield of the bond based on specified market conventions and security structures.
The cash flows of a fixed rate coupon bond consist of periodic coupon rates or coupon payments to the maturity date and the payment of the face value at maturity. The cash flows, also called bond coupon schedules are determined by start accrual date, first coupon date, penultimate date, maturity date, weekend, holidays and market conventions.
The cash flow diagram of s fixed rate bond is shown below, which pays a coupon of value Ci at each date ti, and reimburses the notional V at the maturity date T.
When all coupons have the same value, the ratio R = Ci/V is called the facial rate of the bond. For instance the cash-flow diagram above is drawn wit a 8% facial rate.
The issue date is the day on which the life of a bond starts. The term to maturity defines the period of time, or the life of the bond. The bond’s maturity date is the date on which the last payment is due. The face value (also called par value or principal) of a bond represents the amount that will be repaid to the bondholder at maturity.
The coupon is the nominal annual rate of interest that is paid to the bondholder on a regular basis. It is usually expressed as a percentage of the face value (coupon rate). The coupon rate is either fixed or variable. The coupon rate is given as an annualised percentage of the face value
The coupon period is not necessarily the same for all bonds. The coupon payments are made semi-annually, which is common in the USA, or annually, which is more common in Europe. The coupon payment dates are fixed.
For bonds that pay interest at maturity, the coupon rate is stated as an annualized rate or real rate based on market conventions. Adjustment is made for long/short first/last coupon periods. When a coupon date falls on non-business day, payment may be made next business day with no amount adjustment.
Business day conventions are used to determine when a payment is to be paid. These rules work in conjunction with market calendars. Since calendars vary, the time of the payment also varies, in general. The choice of Business Day conventions is often associated with a specific instrument.
The most common business day conventions are explained as follows:
The Modified convention prevents leaving the current month. The term, “current month”, refers to the month containing the current day; the “next month” refers to the month following the current month; and the “preceding month” refers to the month preceding the current month.
Some bond coupons are daycount based. If the return on a certain security is expressed as an annual return, then the length of a year must be defined precisely. A year may be defined as the actual calendar year, as a certain number of days, or as a certain number of months, each made up of a specified number of days.
To apply standard analytical procedures to interest rates, all time periods applying to the rates and instruments must be expressed in a common unit of measure. To transform period T into a fraction of a year, the number of days in period T are divided by the number of days in one year.
Bond ACT/ACT daycount requires more information than other daycount methods, such as swap ACT/ACT daycount. To calculate the time between two dates, a period date and a payment frequency must be specified. Suppose I want to know the number of years between May 16, 1994 and June 16, 1994, a period of 31 actual days.
For bond ACT/ACT daycount, the answer depends on the start and end date of the accrual period. If the accrual period begins on December 16, 1993 and ends on June 16, 1994 there are 182 days in the period.
Interest accrual calculations for US Treasury bonds use unadjusted period dates. Suppose a US Treasury bond is issued on May 16, 1994, matures on August 20, 1997, and has a short first coupon period. The unadjusted period date for the end of the first coupon period is Saturday, August 20, 1994. The regular coupon period ending on this date begins on Sunday, February 20, 1994 and has 181 days while the short period between May 16 and August 20 has 96 days.
Accrued interest cannot be greater than the total coupon amount. The effective period for bond auction rate is typically one calendar date from that auction up to and including the subsequent auction date.
However, this is subject to a N business day lockout that occurs around issue dates, coupon payment dates, and re-opening issue dates. If the calendar date following the auction lands within N business days of a coupon payment date, issue date or a reopening issue date, then the previous auction rate is applicable up to and including that corresponding issue date, coupon payment date or re-opening issue date.