By Svetlozar T. Račev
The Handbooks in Finance are meant to be a definitive resource for finished and obtainable info within the box of finance. every one person quantity within the sequence should still current a correct self-contained survey of a sub-field of finance, compatible to be used by means of finance and economics professors and academics, specialist researchers, graduate scholars and as a instructing complement. The objective is to have a wide team of exceptional volumes in numerous parts of finance. The guide of Heavy Tailed Distributions in Finance is the 1st guide to be released during this series.
This quantity offers present learn targeting heavy tailed distributions in finance. The contributions conceal methodological matters, i.e., probabilistic, statistical and econometric modelling less than non- Gaussian assumptions, in addition to the purposes of the strong and different non -Gaussian versions in finance and hazard administration.
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Since most VaR calculations are based on the simplifying assumption that the distribution of returns are normal,15 how bad does this assumption effect VaR? Assume that the Profit and Loss (P&L) distribution is symmetric and has finite variance σ 2 . Then regardless of the actual distribution, if X represents the random loss over the specified horizon time with mean zero, Chebyshev’s inequality gives P[X > cσ ] 1 . 071σ . 978σ . 14 See Basle Committee on Banking Supervision (1995a, 1995b). Basle is a city in Switzerland.
Stochastic volatility, power-laws and long memory. Quantitative Finance 1, 427–440. , 2002. Gaussian Self-Affinity and Fractals (Selecta Volume H). Springer-Verlag. , 2003, forthcoming. , 1997. The multifractal model of asset returns. Large deviations and the distribution of price changes. The multifractality of the Deutschmark/US Dollar exchange rate. Discussion Papers numbers 1164, 1165, and 1166 of the Cowles Foundation for Economics at Yale University, New Haven, CT. Available on the web at the following addresses.
X . T T 1 21 RiskMetrics allows the assumption of conditional normality to be relaxed in favor of heavier-tailed conditional distributions. For example the conditional distribution of returns may be mixture of normals or a generalized error distribution, that is, a double sided exponential. O. S. d. mean zero, unit variance random variables representing the innovations of the return process. In the GARCH(p, q) model,22 the conditional variance is given by p σt2 q αi Xt2−i = α0 + i=1 + j =1 βj σt2−j .