Maximum likelihood estimation of stable Paretian models

Stable Paretian distributions have attractive properties for empirical mode ling in finance, because they include the normal distribution as a special case but can also allow for heavier tails and skewness. A major reason for the limited use of stable distributions in applied work is due to the facts that there are, in general, no closed-form expressions for its probability density function and that numerical approximations are nontrivial and comp utationally demanding. Therefore, Maximum Likelihood (ML) estimation of sta ble Paretian models is rather difficult and time consuming. Here, we study the problem of ML estimation using fast Fourier transforms to approximate t he stable density functions. The performance of the ML estimation approach is investigated in a Monte Carlo study and compared to that of a widely use d quantile estimator. Extensions to more general distributional models char acterised by time-varying location and scale are discussed. (C) 1999 Elsevi er Science Ltd. All rights reserved.