Topic
Binomial approximation
About: Binomial approximation is a research topic. Over the lifetime, 844 publications have been published within this topic receiving 23362 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 1950
TL;DR: A First Course in Probability (8th ed.) by S. Ross is a lively text that covers the basic ideas of probability theory including those needed in statistics.
Abstract: Office hours: MWF, immediately after class or early afternoon (time TBA). We will cover the mathematical foundations of probability theory. The basic terminology and concepts of probability theory include: random experiments, sample or outcome spaces (discrete and continuous case), events and their algebra, probability measures, conditional probability A First Course in Probability (8th ed.) by S. Ross. This is a lively text that covers the basic ideas of probability theory including those needed in statistics. Theoretical concepts are introduced via interesting concrete examples. In 394 I will begin my lectures with the basics of probability theory in Chapter 2. However, your first assignment is to review Chapter 1, which treats elementary counting methods. They are used in applications in Chapter 2. I expect to cover Chapters 2-5 plus portions of 6 and 7. You are encouraged to read ahead. In lectures I will not be able to cover every topic and example in Ross, and conversely, I may cover some topics/examples in lectures that are not treated in Ross. You will be responsible for all material in my lectures, assigned reading, and homework, including supplementary handouts if any.
10,221 citations
TL;DR: An analytic solution to the American put problem is derived in this paper, where the hedge ratio and other derivatives of the solution are presented, and a polynomial expression is developed for evaluating these formulae.
Abstract: An analytic solution to the American put problem is derived herein. The hedge ratio and other derivatives of the solution are presented. The formula derived implies an exact duplicating portfolio for the American put consisting of discount bonds and stock sold short. The formula is extended to consider put options on stocks paying cash dividends. A polynomial expression is developed for evaluating these formulae. Values and hedge ratios for puts on both dividend and nondividend paying stocks are calculated, tabulated, and compared with values derived by numerical integration and binomial approximation. As with European options, evaluating an analytic formula is more efficient than approximating the stock price process or the partial differential equation by binomial or finite difference methods. Finally, applications of this American put solution are discussed.
716 citations
611 citations
TL;DR: A binomial approximation to a diffusion is defined as " computationally simple" if the number of nodes grows at most linearly in a number of time intervals as discussed by the authors, and the convergence of the sequence of bond and European option prices from these processes to the corresponding values in the diffusion limit is also demonstrated.
Abstract: A binomial approximation to a diffusion is defined as " computationally simple" if the number of nodes grows at most linearly in the number of time intervals. It is shown how to construct computationally simple binomial processes that converge weakly to commonly employed diffusions in financial models. The convergence of the sequence of bond and European option prices from these processes to the corresponding values in the diffusion limit is also demonstrated. Numerical examples from the constant elasticity of variance stock price and the Cox, Ingersoll, and Ross (1985) discount bond price are provided. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
472 citations
TL;DR: In this paper, the authors extended Ho and Lee's model to include multiple random shocks to the forward rate process and to include an analysis of continuous time limits, and provided insights into the limitations of the existing empirical implementation of Ho-Lee's model.
Abstract: This paper studies the binomial approximation to the continuous trading term structure model of Heath, Jarrow, and Morton (1987). The discrete time approximation makes the original methodology accessible to a wider audience, and provides a computational procedure necessary for calculating the contingent claim values derived in the continuous time paper. This paper also extends and generalizes Ho and Lee's (1986) model to include multiple random shocks to the forward rate process and to include an analysis of continuous time limits. The generalization provides insights into the limitations of the existing empirical implementation of Ho and Lee's model.
402 citations
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Performance Metrics
| Year | Papers |
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| 2025 | 3 |
| 2024 | 4 |
| 2023 | 9 |
| 2022 | 31 |
| 2021 | 1 |
| 2020 | 2 |