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Coupon collector's problem. 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 ...
Component (graph theory) In graph theory, a component of an undirected graph is a connected subgraph that is not part of any larger connected subgraph. The components of any graph partition its vertices into disjoint sets, and are the induced subgraphs of those sets. A graph that is itself connected has exactly one component, consisting of the ...
In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it is a ...
The yield will match the coupon rate when a bond is issued and sold at par value. However, if an investor pays less than the par value, their return would be more significant since the coupon ...
Graphs of n vs E(T) in the coupon collector's problem: Image title: Graphs of the number of coupons, n vs the expected number of tries to collect them, E(T) = ceiling(n H(n)) in the coupon collector's problem, drawn by CMG Lee. Width: 100%: Height: 100%
v. t. e. In finance, bond convexity is a measure of the non-linear relationship of bond prices to changes in interest rates, and is defined as the second derivative of the price of the bond with respect to interest rates ( duration is the first derivative). In general, the higher the duration, the more sensitive the bond price is to the change ...
For example, if a zero-coupon bond with a $20,000 face value and a 20-year term pays 5.5% interest, the interest rate is knocked off the purchase price and the bond might sell for $7,000.
In finance, bootstrapping is a method for constructing a (zero-coupon) fixed-income yield curve from the prices of a set of coupon-bearing products, e.g. bonds and swaps. [ 1 ] A bootstrapped curve , correspondingly, is one where the prices of the instruments used as an input to the curve, will be an exact output , when these same instruments ...