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A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices
Robert C. Blattberg,Nicholas J. Gonedes +1 more
- pp 25-61
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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 SIMULATIONSread more
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Journal ArticleDOI
The Distribution of Share Price Changes
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.
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Parameter Estimates for Symmetric Stable Distributions
Eugene F. Fama,Richard Roll +1 more
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.