Implied volatility is a standard deviation based metric and, while not required, users typically embed the presumption of a bell-shaped curve. Starting with implied volatility, the risk manager or financial analyst then must work to augment the tails of the probability distribution to increase the ...
A general model for bivariate tails probability We study bivariate stochastic recurrence equations with triangular matrix coefficients and we characterize the tail behavior of their stationary solutions {\\bf W} =(W_1,W_2) {\\bf W} =(W_1,W_2) . Recently it has been observed that W_1,...
Misestimating Probability Distributions of Repeated Events Oleg Urminsky (oleg.urminsky@chicagobooth.edu) University of Chicago, 5807 S. Woodlawn Ave Chicago, IL 60637 USA Abstract This paper examines people鈥檚 subjective beliefs about probabil- ity distributions arising from repeated events, such as...
The fractal dimension can also be inferred from the probability distribution of the first neighbour14. Finally, Nearest Neighbors-Based ID estimators describe data neighborhoods distributions as functions of the intrinsic dimension d, usually assuming that close points are uniformly drawn from small ...
Annals of the Institute of Statistical MathematicsYanagimoto, T. and Sibuya, M. Comparison of tails of distributions in models for estimating safe doses, Ann. Inst. Statist. Math. , 32 , A, 325–340.T. Yanagimoto, M. Sibuya, Comparison of tails of distributions in models for estimating...
This paper presents a new approach to estimating the conditional probability distribution of multiperiod financial returns. Estimation of the tails of the distribution is particularly important for risk management tools, such as Value-at-Risk models. A popular approach is to assume a Gaussian ...
Statistics & Probability LettersE. G. Tsionas, "Estimating multivariate heavy tails and principal directions easily, with an application to international exchange rates," Statistics and Probability Letters, vol. 82, no. 11, pp. 1986- 1989, 2012....
We observe that a number of well-known power-law models, including the exponential, Pareto, Student-t, and skewed generalized-t (SGT) distributions, are special cases of the family of power-law probability densities that we consider. We benchmark our method against state-of-the-art asset ...
It is argued that the study of the correct specification of returns distributions has attractive implications in financial economics. This study estimates Levy-stable (fractal) distributions that can accurately account for skewness, kurtosis, and fat tails. The Levy-stable family distributions are ...
Statistical distributionsDecision theorySamplingAnalysis of variancePolynomialsProbabilityTablesThe purpose of this note is to present a moment estimator for the parameter of the geometric distribution from samples which are truncated at arbitrary points in either or both tails of the distribution. This is...