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In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more than t boxes need to be bought ...
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 value of $1,000 and a coupon rate of 5%, then it pays total coupons of $50 per year.
Analytic Example: Given: 0.5-year spot rate, Z1 = 4%, and 1-year spot rate, Z2 = 4.3% (we can get these rates from T-Bills which are zero-coupon); and the par rate on a 1.5-year semi-annual coupon bond, R3 = 4.5%. We then use these rates to calculate the 1.5 year spot rate. We solve the 1.5 year spot rate, Z3, by the formula below:
Is there a name for, or any research on this specific variant of the coupon collector's problem?Specifically, I am looking for a formula that calculates the expected number of batches we need to draw in order to collect all N kinds of coupons, given that in one batch there are k coupons that are not necessarily different (we can for example get a batch of 10 same coupons).
A corporate bond has a coupon rate of 7.2% and pays 4 times a year, on 15 January, April, July, and October. It uses the 30/360 US day count convention. A trade for 1,000 par value of the bond settles on January 25. The prior coupon date was January 15. The accrued interest reflects ten days' interest, or $2.00 = (7.2% of $1,000 * (10 days/360 ...
Some debt instruments leverage the particular effects of interest rate changes, most commonly in inverse floaters. [2] As an example, an inverse floater with a multiple may pay interest a rate, or coupon, of 22 percent minus the product of 2 times the 30-day SOFR (Secured Overnight Financing Rate). [3] The coupon leverage is 2, in this example.
Here’s an example using the $100,000 loan with a factor rate of 1.5 and a two-year (730 days) repayment period: Step 1: 1.50 – 1 = 0.50 Step 2: .50 x 365 = 182.50
With an inverse floater, as interest rates rise the coupon rate falls. [1] The basic structure is the same as an ordinary floating rate note except for the direction in which the coupon rate is adjusted. These two structures are often used in concert. As short-term interest rates fall, both the market price and the yield of the inverse floater ...