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A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices
01 Jan 2010-pp 25-61
TL;DR: In this article, the student and stable models were used to compare the rates of return of different stock price models, including the Student Distribution and the Stable Distribution, in terms of the Likelihood Ratio and the Fama-Roll.
Abstract: The following sections are included:INTRODUCTIONPROPERTIES OF THE STUDENT AND SYMMETRIC-STABLE DISTRIBUTIONSDefinitions and Properties of the Student and Stable ModelsSome Implications of the Student and Stable Models for Empirical and Theoretical WorkAdditional RemarksMODELS FOR RATES OF RETURNDerivation of the Student and Stable Models: SummaryOther Stock Price ModelsMETHODS FOR MODEL COMPARISONThe Likelihood RatioStabilityESTIMATION OF THE MODEL'S PARAMETERSM.L.E. for the Student DistributionFama-Roll Estimates for the Stable DistributionESTIMATION RESULTSThe Actual DataThe Design of the Monte Carlo StudyDiscussion of the Simulation ResultsResults for Rates of ReturnSUMMARYAPPENDIX A DERIVATIONS OF THE STUDENT AND STABLE MODELSAPPENDIX B PROPERTIES OF THE UNIFORM RANDOM NUMBERS USED IN THE SIMULATIONS
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TL;DR: In this paper, the authors examine properties of daily stock returns and how the particular characteristics of these data affect event study methodologies and show that recognition of autocorrelation in daily excess returns and changes in their variance conditional on an event can sometimes be advantageous.
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TL;DR: In this paper, a new stochastic process, termed the variance gamma process, is proposed as a model for the uncertainty underlying security prices, which is normal conditional on a variance, distributed as a gamma variate.
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TL;DR: In this article, the stock price distributions that arise when prices follow a diffusion process with a stochastically varying volatility parameter are studied, and an explicit closed-form solution for the case where volatility is driven by an arithmetic Ornstein-Ublenbeck (or AR1) process is derived.
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TL;DR: In this paper, the authors presented both theoretical and empirical evidence about a probability distribution which describes the behavior of share price changes, which is the only known simple distribution to fit changes in share prices, and provided a far better fit to the data than the stable Paretian, compound process, and normal distributions.
Abstract: This paper presents both theoretical and empirical evidence about a probability distribution which describes the behavior of share price changes. Osborne's Brownian motion theory of share price changes is modified to account for the changing variance of the share market. This produces a scaled t-distribution which is an excellent fit to series of share price indices. This distribution is the only known simple distribution to fit changes in share prices. It provides a far better fit to the data than the stable Paretian, compound process, and normal distributions.
557 citations
TL;DR: In this paper, estimators for the scale parameter and characteristic exponent of symmetric stable distributions are proposed and Monte Carlo studies of these estimators are reported. And the powers of various goodness-of-fit tests of a Gaussian null hypothesis against non-Gaussian stable alternatives are also investigated.
Abstract: Building on results of an earlier article [6], estimators are suggested for the scale parameter and characteristic exponent of symmetric stable distributions, and Monte Carlo studies of these estimators are reported. The powers of various goodness-of-fit tests of a Gaussian null hypothesis against non-Gaussian stable alternatives are also investigated. Finally, a test of the stability property of symmetric stable variables is suggested and demonstrated.
529 citations