Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Power-law tail behavior and the summation scheme of Levy-stable (alpha- stable) distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0Levy-stable distribution, Alpha-stable distribution, Tail exponent, Hill estimator

Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime (0Levy-stable distribution; Alpha-stable distribution; Tail exponent; Hill estimator;

Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime

Power-law tail behavior and the summation scheme of Levy-stable distributions is the basis for their frequent use as models when fat tails above a Gaussian distribution are observed. However, recent studies suggest that financial asset returns exhibit tail exponents well above the Levy-stable regime ($0<\alpha\le 2$). In this paper we illustrate that widely used tail index estimates (log-log linear regression and Hill) can give exponents well above the asymptotic limit for $\alpha$ close to 2, resulting in overestimation of the tail exponent in finite samples. The reported value of the tail exponent $\alpha$ around 3 may very well indicate a Levy-stable distribution with $\alpha\approx 1.8$.Comment: To be published in Int. J. Modern Physics C (2001) vol. 12 no.

Power Law Signature in Indonesian Population

The paper analyzes the spreading of population in Indonesia. The spreading of population in Indonesia is clustered in two regional terms, i.e.: kabupaten and kotamadya. It is interestingly found that the rank in all kabupaten respect to the population does not have fat tail properties, while in the other hand; there exists power-law signature in kotamadya. We analyzed that this fact could be caused by the equal or similar infrastructural development in all regions; nevertheless, we also note that the first 20 kabupatens are dominated in Java and Sumatera. Furthermore, the fat tail character in the rank of kotamadya could be caused by the big gap between big cities one another, e.g.: Jakarta, Surabaya, and others. The paper ends with some suggestions of more attention to infrastructural development in eastern regional cities

Fat-Tail Distributions and Business-Cycle Models

Recent empirical findings suggest that macroeconomic variables are seldom normally distributed. For example, the distributions of aggregate output growth-rate time series of many OECD countries are well approximated by symmetric exponential-power (EP) densities, with Laplace fat tails. In this work, we assess whether Real Business Cycle (RBC) and standard medium-scale New-Keynesian (NK) models are able to replicate this statistical regularity. We simulate both models drawing Gaussian- vs Laplace-distributed shocks and we explore the statistical properties of simulated time series. Our results cast doubts on whether RBC and NK models are able to provide a satisfactory representation of the transmission mechanisms linking exogenous shocks to macroeconomic dynamics.Growth-Rate Distributions, Normality, Fat Tails, Time Series, Exponential-Power Distributions, Laplace Distributions, DSGE Models, RBC Models

Fat-tail Distributions and Business-Cycle Models

Recent empirical findings suggest that macroeconomic variables are seldom normally dis- tributed. For example, the distributions of aggregate output growth-rate time series of many OECD countries are well approximated by symmetric exponential-power (EP) den- sities, with Laplace fat tails. In this work, we assess whether Real Business Cycle (RBC) and standard medium-scale New-Keynesian (NK) models are able to replicate this sta- tistical regularity. We simulate both models drawing Gaussian- vs Laplace-distributed shocks and we explore the statistical properties of simulated time series. Our results cast doubts on whether RBC and NK models are able to provide a satisfactory representation of the transmission mechanisms linking exogenous shocks to macroeconomic dynamics.Growth-Rate Distributions, Normality, Fat Tails, Time Series, Exponential- Power Distributions, Laplace Distributions, DSGE Models, RBC Models.

Comparative Analyses of Expected Shortfall and Value-at-Risk (3): Their Validity under Market Stress

In this paper, we compare value-at-risk (VaR) and expected shortfall under market stress. Assuming that the multivariate extreme value distribution represents asset returns under market stress, we simulate asset returns with this distribution. With these simulated asset returns, we examine whether market stress affects the properties of VaR and expected shortfall. Our findings are as follows. First, VaR and expected shortfall may underestimate the risk of securities with fat- tailed properties and a high potential for large losses. Second, VaR and expected shortfall may both disregard the tail dependence of asset returns. Third, expected shortfall has less of a problem in disregarding the fat tails and the tail dependence than VaR does.

The Unholy Trinity: Fat Tails, Tail Dependence, and Micro-Correlations

Recent events in the financial and insurance markets, as well as the looming challenges of a globally changing climate point to the need to re-think the ways in which we measure and manage catastrophic and dependent risks. Management can only be as good as our measurement tools. To that end, this paper outlines detection, measurement, and analysis strategies for fat-tailed risks, tail dependent risks, and risks characterized by micro-correlations. A simple model of insurance demand and supply is used to illustrate the difficulties in insuring risks characterized by these phenomena. Policy implications are discussed.risk, fat tails, tail dependence, micro-correlations, insurance, natural disasters

Extreme risk in Asian equity markets

Extreme price movements associated with tail returns are catastrophic for all investors and it is necessary to make accurate predictions of the severity of these events. Choosing a time frame associated with large financial booms and crises this paper investigates the tail behaviour of Asian equity market returns and quantifies two risk measures, quantiles and average losses, along with their associated average waiting periods. Extreme value theory using the Peaks over Threshold method generates the risk measures where tail returns are modelled with a fat-tailed Generalised Pareto Distribution. We find that lower tail risk measures are more severe than upper tail realisations at the lowest probability levels. Moreover, the Kuala Lumpar Composite exhibits the largest risk measures.