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Abstract:
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Stable distributions have long been used as models to describe financial asset returns such as logarithmic changes in the price of stocks. The flexibility of allowing both skewness and heavy tails in addition to location and scale parameters makes this rich class of probability distributions extremely important in financial risk management and portfolio selection via the optimal allocation of assets between Gaussian and non-Gaussian stable distribution portfolios. However, the lack of closed-form formulae for densities and distribution functions for the full parameter range has limited the wide use of stable distributions by practitioners. Despite extensive research, accurate estimation of model parameters such as the tail index remains elusive. In this paper, we propose a simple yet remarkably accurate method for estimating general stable distributions. We present a globally convergent algorithm for estimating the tail index. In addition, we demonstrate the performance of the method by simulations and illustrate its usefulness in financial applications.
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