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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 ...
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. Typically, this will consist of two semi-annual payments of $25 each. [3] 1945 2.5% $500 Treasury Bond coupon
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).
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:
Price example: XYZ Ltd. issues a bond with a $1000 face value and a $980 published price, with a coupon rate of 5% paid semi-annually and a maturity date of five years. The annual coupon payment is 5% of $1000, or $50. The investor receives a $25 coupon payment every six months until the maturity date.
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.
Interest rate risk is the risk that arises for bond owners from fluctuating interest rates. How much interest rate risk a bond has depends on how sensitive its price is to interest rate changes in the market. The sensitivity depends on two things, the bond's time to maturity, and the coupon rate of the bond. [1]
The Hammett equation predicts the equilibrium constant or reaction rate of a reaction from a substituent constant and a reaction type constant. The Edwards equation relates the nucleophilic power to polarisability and basicity. The Marcus equation is an example of a quadratic free-energy relationship (QFER). [citation needed]