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ABSTRACT: Estimation of the tail index of stationary, fat-tailed return distributions is non-trivial since the well-known Hill estimator
is optimal only under iid draws from an exact Pareto model. We provide a small sample simulation study of recently suggested
adaptive estimators under ARCH-type dependence. The Hill estimator’s performance is found to be dominated by a ratio estimator.
Dependence increases estimation error which can remain substantial even in larger data sets. As small sample bias is related
to the magnitude of the tail index, recent standard applications may have overestimated (underestimated) the risk of assets
with low (high) degrees of fat-tailedness.
Statistical Papers 04/2012; 45(4):545-561. · 0.59 Impact Factor
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ABSTRACT: With the celebrated model of Black and Scholes in 1973 the development of modern option pricing models started. One of the assumptions of the Black and Scholes model ist that the risky asset evolves according to the geometric brownian motion which implies normal distributed returns. As empirical investigations show, the stock returns do not follow a normal distributions, but are leptokurtic and to some extend skewed. The following paper proposes so-called Esscher-EGB2 option pricing model, where the price process is modeled by an exponential EGB2-Levy-motion, implying that the returns follow an EGB2 distribution and the equivalent martingale measure is given by the Esscher transformation --
EconWPA, Econometrics. 01/2004;
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ABSTRACT: Accurate modeling of extremal price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including GARCH and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias strongly relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail-thickness due to small sample bias. As a consequence, high quantile estimation may lead to a substantial underestimation of tail risk.
Research Program in Finance, Institute for Business and Economic Research, UC Berkeley, Research Program in Finance, Working Paper Series. 01/2003;
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ABSTRACT: This paper reconsiders return-volume dependence for the U.S. and six international equity markets. We contribute to previous work by proposing surprise volume as a new proxy for private information flow and apply extreme value theory in studying dependence for large volume and return, i.e. under situations of market stress. Results from a GARCH-M model indicate that surprise volume is superior in explaining conditional variance and reveals a positive market risk premium. Under conditions of market stress, the return-volume dependence is weaker, albeit mostly significant. The results for the U.S. market are most pronounced in that surprise volume explains ARCH- as well as leverage-effects and, under market stress, the return-volume dependence remains significant and symmetric. For the European and Asian markets, however, the dependence is weaker with asymmetry under market stress, i.e. small minimal returns show lower volume dependence than large maximal returns. We argue that our results are more consistent with a Gennotte and Leland (1990) misinterpretation hypothesis for market crashes than with cascade or behavioral explanations which associate high volume with steep price declines.
Research Program in Finance, Institute for Business and Economic Research, UC Berkeley, Research Program in Finance, Working Paper Series. 01/2003;
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ABSTRACT: Accurate modeling of extreme price changes is vital to financial risk management. We examine the small sample properties of adaptive tail index estimators under the class of student-t marginal distribution functions including generalized autoregressive conditional heteroskedastic (GARCH) models and propose a model-based bias-corrected estimation approach. Our simulation results indicate that bias relates to the underlying model and may be positively as well as negatively signed. The empirical study of daily exchange rate changes reveals substantial differences in measured tail thickness due to small sample bias. Thus, high quantile estimation may lead to a substantial underestimation of tail risk.
Journal of Empirical Finance.
