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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] For example, if a bond has a face ...
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 ...
The spread is a rate that remains constant. Almost all FRNs have quarterly coupons, i.e. they pay out interest every three months. At the beginning of each coupon period, the coupon is calculated by taking the fixing of the reference rate for that day and adding the spread. [1] [2] [3] A typical coupon would look like 3 months USD SOFR +0.20%.
the length of time over which the bond produces cash flows for the investor (the maturity date of the bond), interest earned on reinvested coupon payments, or reinvestment risk (the uncertainty about the rate at which future cash flows can be reinvested), and; fluctuations in the market price of a bond prior to maturity. [3]
Consider first a $100 investment in each, which makes sense for the three bonds (the coupon bond, the annuity, the zero-coupon bond - it does not make sense for the interest rate swap for which there is no initial investment). Modified duration is a useful measure to compare interest rate sensitivity across the three.
For example, you might pay $5,000 for a zero-coupon bond with a face value of $10,000 and receive the full price, $10,000, upon maturity in 20 or 30 years. Zero-coupon CDs work the same way.
Because interest rate caps/floors are equivalent to bond puts and calls respectively, the above analysis shows that caps and floors can be priced analytically in the Hull–White model. Jamshidian's trick applies to Hull–White (as today's value of a swaption in the Hull–White model is a monotonic function of today's short rate). Thus ...
Duration is a linear measure of how the price of a bond changes in response to interest rate changes. It is approximately equal to the percentage change in price for a given change in yield, and may be thought of as the elasticity of the bond's price with respect to discount rates. For example, for small interest rate changes, the duration is ...