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Encyclopedia of Financial Models, 3 Volume Set by Frank J. Fabozzi

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Fat Tails, Scaling, and Stable Laws

SERGIO M. FOCARDI, PhD

Partner, The Interteak Group

FRANK J. FABOZZI, PhD, CFA, CPA

Professor of Finance, EDHEC Business School

Abstract: Fat-tailed laws have been found in many economic variables. Fully approximating a finite economic system with fat-tailed laws depends on an accurate statistical analysis of the phenomena, but also on a number of the theoretical implications of subexponentiality and scaling. Modeling financial variables with stable laws implies the assumption of infinite variance, which seems to contradict empirical observations. Nevertheless, scaling laws might still be an appropriate modeling paradigm given the complex interaction of distributional shape and correlations in price processes. They might help in understanding not only the sheer size of economic fluctuations but also the complexity of economic cycles. There are applications where scaling laws play a fundamental role, in particular in risk management and financial optimization. Ignoring the possibility of large deviations would render financial risk management ineffective and dangerous.

Most models of stochastic processes and time series assume that distributions have finite mean and finite variance. In this entry we describe fat-tailed distributions with infinite variance. Fat-tailed distributions have been found in many financial economic variables ranging from forecasting returns on financial assets to modeling recovery distributions in bankruptcies. They ...

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