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In finance, a coupon is the interest payment received by a bondholder from the date of issuance until the date of maturity of a bond. [ 1 ] Coupons are normally described in terms of the "coupon rate", which is calculated by adding the sum of coupons paid per year and dividing it by the bond's face value . [ 2 ]
The full Laplace transform is the curve of all present values, plotted as a function of interest rate. For discrete time, where payments are separated by large time periods, the transform reduces to a sum, but when payments are ongoing on an almost continual basis, the mathematics of continuous functions can be used as an approximation.)
The formula for the present value of a regular stream of future payments (an annuity) is derived from a sum of the formula for future value of a single future payment, as below, where C is the payment amount and n the period. A single payment C at future time m has the following future value at future time n:
a = fraction of a period remaining until next coupon payment; m = number of full coupon periods until maturity; P = bond price (present value of cash flows discounted with rate i) For a bond with coupon frequency but an integer number of periods (so that there is no fractional payment period), the formula simplifies to: [25]
To separate out the effect of the coupon payments, the accrued interest between coupon dates is subtracted from the value determined by the dirty price to arrive at the clean price. [1] The accrued interest is based on the day count convention , coupon rate, and number of days from the preceding coupon payment date.
Future value is the value of an asset at a specific date. [1] It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain interest rate , or more generally, rate of return ; it is the present value multiplied by the accumulation function . [ 2 ]
Starting date for the accrual. It is usually the coupon payment date preceding Date2. Date2 (Y2.M2.D2) Date through which interest is being accrued. You could word this as the "to" date, with Date1 as the "from" date. For a bond trade, it is the settlement date of the trade. Date3 (Y3.M3.D3) Is the next coupon payment date, usually it is close ...
To extract the forward rate, we need the zero-coupon yield curve.. We are trying to find the future interest rate , for time period (,), and expressed in years, given the rate for time period (,) and rate for time period (,).