Topic
Binomial (polynomial)
About: Binomial (polynomial) is a research topic. Over the lifetime, 2005 publications have been published within this topic receiving 27883 citations. The topic is also known as: binomial.
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4,095 citations
TL;DR: In this article, a new method for inferring risk-neutral probabilities (or state-contingent prices) from the simultaneously observed prices of European options is developed. But this method requires the assumption that the underlying asset has a limited risk-free lognormal distribution.
Abstract: This article develops a new method for inferring risk-neutral probabilities (or state-contingent prices) from the simultaneously observed prices of European options. These probabilities are then used to infer a unique fully specified recombining binomial tree that is consistent with these probabilities (and, hence, consistent with all the observed option prices). A simple backwards recursive procedure solves for the entire tree. From the standpoint of the standard binomial option pricing model, which implies a limiting risk-neutral lognormal distribution for the underlying asset, the approach here provides the natural (and probably the simplest) way to generalize to arbitrary ending risk-neutral probability distributions.
1,858 citations
TL;DR: In this paper, a combinatorial interpretation for any minor (or binomial determinant) of the matrix of binomial coefficients is given, involving configurations of nonintersecting paths, and is related to Young tableaux and hook length formulae.
825 citations
01 Jan 1979
TL;DR: In this paper, non-parametric techniques are introduced for the change-point problem and exact and approximate results are obtained for testing the null hypothesis of no change for zero-one observations, Binomial observations and continuous observations.
Abstract: SUMMARY Non-parametric techniques are introduced for the change-point problem. Exact and approximate results are obtained for testing the null hypothesis of no change. The methods are illustrated by the analysis of three sets of data illustrating the techniques for zero-one observations, Binomial observations and continuous observations. Some comparisons are made with methods based on CUSUMS.
768 citations
TL;DR: In this paper, the volume and number of lattice points of the permutohedron Pn are given by certain multivariate polynomials that have remarkable com- binatorial properties.
Abstract: The volume and the number of lattice points of the permutohedron Pn are given by certain multivariate polynomials that have remarkable com- binatorial properties. We give 3 dieren t formulas for these polynomials. We also study a more general class of polytopes that includes the permutohedron, the associahedron, the cyclohedron, the Stanley-Pitman polytope, and various generalized associahedra related to wonderful compactications of De Concini- Procesi. These polytopes are constructed as Minkowsky sums of simplices. We calculate their volumes and describe their combinatorial structure. The coef- cien ts of monomials in Vol Pn are certain positive integer numbers, which we call the mixed Eulerian numbers. These numbers are equal to the mixed volumes of hypersimplices. Various specializations of these numbers give the usual Eulerian numbers, the Catalan numbers, the numbers (n+1) n 1 of trees (or parking functions), the binomial coecien ts, etc. We calculate the mixed Eulerian numbers using certain binary trees. Many results are extended to an arbitrary Weyl group.
535 citations