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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 ...
There is a map from a curve to its dual, sending each point to the point dual to its tangent line. If C is algebraic then so is its dual and the degree of the dual is known as the class of the original curve. The equation of the dual of C, given in line coordinates, is known as the tangential equation of C.
Tree returning the OAS (black vs red): the short rate is the top value; the development of the bond value shows pull-to-par clearly . A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written .
Forward rate / Forward curve-based models (Application as per short-rate models) LIBOR market model (also called: Brace–Gatarek–Musiela Model, BGM) Heath–Jarrow–Morton Model (HJM) Cheyette model; Valuation adjustments Credit valuation adjustment; XVA; Yield curve modelling Multi-curve framework; Bootstrapping (finance)
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A curve in this context is defined by a non-degenerate algebraic equation in the complex projective plane.Lines in this plane correspond to points in the dual projective plane and the lines tangent to a given algebraic curve C correspond to points in an algebraic curve C * called the dual curve.
The dual graph is a representation of how variables are constrained in the dual problem. More precisely, the dual graph contains a node for each dual variable and an edge for every constraint between them. In addition, the edge between two variables is labeled by the original variables that are enforced equal between these two dual variables.
Isotonic regression has applications in statistical inference.For example, one might use it to fit an isotonic curve to the means of some set of experimental results when an increase in those means according to some particular ordering is expected.