Estimation of Stable Law Parameters: Stock Price Behavior Application

Abstract A point of considerable interest is whether the asymmetric stable laws rather than the symmetric stable laws provide for a closer representation of the behavior of security prices. Our empirical results indicate that the asymmetric laws are more appropriate than the symmetric stable laws. A new estimation procedure is used to obtain the estimates of parameters of the stable laws for 20 randomly selected stocks from the New York Stock Exchange. Estimates of the skewness parameter are explicitly obtained for the first time. The estimates are compared with those obtained under the assumption of symmetry and are also compared with the estimates provided by the method of Fama and Roll [13].

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