Continuity Correction
نویسنده
چکیده
According to the central limit theorem (CLT ), the distribution function Fn of a normalized sum n(X1 + ... + Xn) of n independent random variables X1, ..., Xn , having a common distribution with mean zero and variance σ 2 > 0, converges to the distribution function Φσ of the normal distribution with mean zero and variance σ, as n → ∞. We will write Φ for Φ1 for the case σ = 1. The densities of Φσ and Φ are denoted by φσ and φ, respectively. In the case X ′ js are discrete, Fn has jumps and the normal approximation is not very good when n is not sufficiently large. This is a problem which most commonly occurs in statistical tests and estimation involving the normal approximation to the binomial and, in its multi-dimensional version, in Pearson’s frequency chisquare tests, or in tests for association in categorical data. Applying the CLT to a binomial random variable T with distribution B(n, p), with mean np and variance npq(q = 1 − p), the normal approximation is given , for integers 0 ≤ a ≤ b ≤ n, by P (a ≤ T ≤ b) ≈ Φ((b− np)/√npq)− Φ((a− np)/√npq). (1)
منابع مشابه
A Note on the Kou’s Continuity Correction Formula
This article introduces a hyper-exponential jump diffusion process based on the continuity correction for discrete barrier options under the standard B-S model, using measure transformation and stopping time theory to prove the correction, thus broadening the conditions of the continuity correction of Kou.
متن کاملYates and Contingency Tables: 75 Years Later
Seventy-five years ago, Yates (1934) presented an article introducing his continuity correction to the χ test for independence in contingency tables. The paper also was one of the first introductions to Fisher’s exact test. We discuss the historical importance of Yates and his 1934 paper. The development of the exact test and continuity correction are studied in some detail. Subsequent disputes...
متن کاملA matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 2: Bermudan options
We discuss the ‘continuity correction’ that should be applied to connect the prices of discretely sampled American put options (i.e. Bermudan options) and their continuously-sampled equivalents. Using a matched asymptotic expansions approach we compute the correction and relate it to that discussed by Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) for barrier options. In the Ber...
متن کاملA matched asymptotic expansions approach to continuity corrections for discretely sampled options. Part 1: barrier options
We discuss the ‘continuity correction’ that should be applied to relate the prices of discretely sampled barrier options and their continuouslysampled equivalents. Using a matched asymptotic expansions approach we show that the correction of Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) can be applied in a very wide variety of cases. We calculate the correction to higher order ...
متن کاملDiscrete Barrier and Lookback Options
Discrete barrier and lookback options are among the most popular path-dependent options in markets. However, due to the discrete monitoring policy almost no analytical solutions are available for them. We shall focus on the following methods for discrete barrier and lookback option prices: (1) Broadie–Yamamoto method based on fast Gaussian transforms. (2) Feng–Linetsky method based on Hilbert t...
متن کامل