scholarly journals Tail Behavior and Dependence Structure in the APARCH Model

2016 ◽  
Vol 9 (2) ◽  
Author(s):  
Farrukh Javed ◽  
Krzysztof Podgórski
Keyword(s):  
Statistical Inference ◽  
Dependence Structure ◽  
Leverage Effect ◽  
Tail Behavior ◽  
News Shocks ◽  
Negative News ◽  
Asymmetric Responses ◽  
Heavy Tailed ◽  
European Economies ◽  
Theoretical Results

AbstractThe APARCH model attempts to capture asymmetric responses of volatility to positive and negative ‘news shocks’ – the phenomenon known as the leverage effect. Despite its potential, the model’s properties have not yet been fully investigated. While the capacity to account for the leverage is clear from the defining structure, little is known how the effect is quantified in terms of the model’s parameters. The same applies to the quantification of heavy-tailedness and dependence. To fill this void, we study the model in further detail. We study conditions of its existence in different metrics and obtain explicit characteristics: skewness, kurtosis, correlations and leverage. Utilizing these results, we analyze the roles of the parameters and discuss statistical inference. We also propose an extension of the model. Through theoretical results we demonstrate that the model can produce heavy-tailed data. We illustrate these properties using S&P500 data and country indices for dominant European economies.

scholarly journals Asymptotics for ultimate ruin probability in a by-claim risk model

2021 ◽  
Vol 26 (2) ◽  
pp. 259-270
Author(s):  
Aili Zhang ◽  
Shuang Liu ◽  
Yang Yang
Keyword(s):  
Ruin Probability ◽  
Risk Model ◽  
Asymptotic Formulas ◽  
Dependence Structure ◽  
Simulation Studies ◽  
Main Claim ◽  
Heavy Tailed ◽  
Constant Interest Rate ◽  
Constant Interest ◽  
Theoretical Results

This paper considers a by-claim risk model with constant interest rate in which the main claim and by-claim random vectors form a sequence of independent and identically distributed random pairs with each pair obeying some certain dependence or arbitrary dependence structure. Under the assumption of heavy-tailed claims, we derive some asymptotic formulas for ultimate ruin probability. Some simulation studies are also performed to check the accuracy of the obtained theoretical results via the crude Monte Carlo method.

scholarly journals Extremal behavior of Archimedean copulas

2011 ◽  
Vol 43 (1) ◽  
pp. 195-216 ◽  
Author(s):  
Martin Larsson ◽  
Johanna Nešlehová
Keyword(s):  
Domain Of Attraction ◽  
Tail Dependence ◽  
Dependence Structure ◽  
Tail Behavior ◽  
Archimedean Copulas ◽  
Radial Part ◽  
Stochastic Representation ◽  
Lower Tail ◽  
Extremal Behavior ◽  
Practical Implications

We show how the extremal behavior of d-variate Archimedean copulas can be deduced from their stochastic representation as the survival dependence structure of an ℓ1-symmetric distribution (see McNeil and Nešlehová (2009)). We show that the extremal behavior of the radial part of the representation is determined by its Williamson d-transform. This leads in turn to simple proofs and extensions of recent results characterizing the domain of attraction of Archimedean copulas, their upper and lower tail-dependence indices, as well as their associated threshold copulas. We outline some of the practical implications of their results for the construction of Archimedean models with specific tail behavior and give counterexamples of Archimedean copulas whose coefficient of lower tail dependence does not exist.

scholarly journals Large Deviations for a Class of Multivariate Heavy-Tailed Risk Processes Used in Insurance and Finance

2021 ◽  
Vol 14 (5) ◽  
pp. 202
Author(s):  
Miriam Hägele ◽  
Jaakko Lehtomaa
Keyword(s):  
Large Deviations ◽  
Risk Sharing ◽  
Dependence Structure ◽  
Large Deviations Principle ◽  
Shape Constraint ◽  
Multiple Components ◽  
Insurance Portfolio ◽  
Heavy Tailed ◽  
Tail Events ◽  
Risk Processes

Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the main problems is to decide if there is any type of dependence between the components of the vector and, if so, what type of dependence structure should be used for accurate modelling. We study a class of heavy-tailed multivariate random vectors under a non-parametric shape constraint on the tail decay rate. This class contains, for instance, elliptical distributions whose tail is in the intermediate heavy-tailed regime, which includes Weibull and lognormal type tails. The study derives asymptotic approximations for tail events of random walks. Consequently, a full large deviations principle is obtained under, essentially, minimal assumptions. As an application, an optimisation method for a large class of Quota Share (QS) risk sharing schemes used in insurance and finance is obtained.

scholarly journals Asymptotic Behavior of Ruin Probabilities in an Insurance Risk Model with Quasi-Asymptotically Independent or Bivariate Regularly Varying-Tailed Main Claim and By-Claim

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Yang Yang ◽  
Xinzhi Wang ◽  
Xiaonan Su ◽  
Aili Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Risk Model ◽  
Dependence Structure ◽  
Ruin Probabilities ◽  
Insurance Risk ◽  
Main Claim ◽  
Regularly Varying ◽  
Heavy Tailed ◽  
Insurance Risk Model

This paper considers a by-claim risk model under the asymptotical independence or asymptotical dependence structure between each main claim and its by-claim. In the presence of heavy-tailed main claims and by-claims, we derive some asymptotic behavior for ruin probabilities.

STATISTICAL INFERENCE FOR MEASUREMENT EQUATION SELECTION IN THE LOG-REALGARCH MODEL

2018 ◽  
Vol 35 (05) ◽  
pp. 943-977 ◽  
Author(s):  
Yu-Ning Li ◽  
Yi Zhang ◽  
Caiya Zhang
Keyword(s):  
Statistical Inference ◽  
Asymptotic Results ◽  
Measurement Equation ◽  
Inference Problem ◽  
Consistency Test ◽  
Sufficient And Necessary Conditions ◽  
Quasi Maximum Likelihood ◽  
Strict Stationarity ◽  
Self Consistency ◽  
Theoretical Results

This article investigates the statistical inference problem of whether a measurement equation is self-consistent in the logarithmic realized GARCH model (log-RealGARCH). First, we provide the sufficient and necessary conditions for the strict stationarity of both the log-RealGARCH model and the log-GARCH-X model. Under these conditions, strong consistency and asymptotic normality of the quasi-maximum likelihood estimators of these two models are obtained. Then, based on the asymptotic results, we propose a Hausman-type self-consistency test for diagnosing the suitability of the measurement equation in the log-RealGARCH model. Finally, the results of simulations and an empirical study are found to accord with the theoretical results.

scholarly journals Leverage Effect for Volatility with Generalized Laplace Error

2014 ◽  
Vol 29 (2) ◽  
Author(s):  
Farrukh Javed ◽  
Krzysztof Podgórski
Keyword(s):  
Good News ◽  
Leverage Effect ◽  
Economic Time Series ◽  
News Shocks ◽  
Fundamental Properties ◽  
The Past ◽  
Volatility Models ◽  
Asymmetric Power ◽  
Power Models ◽  
Economic Time

AbstractWe propose a new model that accounts for the asymmetric response of volatility to positive (`good news') and negative (`bad news') shocks in economic time series – the so-called leverage effect. In the past, asymmetric powers of errors in the conditionally heteroskedastic models have been used to capture this effect. Our model is using the gamma difference representation of the generalized Laplace distributions that efficiently models the asymmetry. It has one additional natural parameter, the shape, that is used instead of power in the asymmetric power models to capture the strength of a long-lasting effect of shocks. Some fundamental properties of the model are provided including the formula for covariances and an explicit form for the conditional distribution of `bad' and `good' news processes given the past – the property that is important for statistical fitting of the model. Relevant features of volatility models are illustrated using S&P 500 historical data.

scholarly journals Statistical inference in regression with heavy-tailed integrated variables

2001 ◽  
Vol 34 (9-11) ◽  
pp. 1145-1158 ◽  
Author(s):  
S. Mittnik ◽  
V. Paulauskas ◽  
S.T. Rachev
Keyword(s):  
Statistical Inference ◽  
Heavy Tailed

Tail behavior of the sums of dependent and heavy-tailed random variables

2015 ◽  
Vol 44 (1) ◽  
pp. 12-27 ◽  
Author(s):  
Changjun Yu ◽  
Yuebao Wang ◽  
Dongya Cheng
Keyword(s):  
Random Variables ◽  
Tail Behavior ◽  
Heavy Tailed

scholarly journals On the foundations of multivariate heavy-tail analysis

2004 ◽  
Vol 41 (A) ◽  
pp. 191-212 ◽  
Author(s):  
Sidney Resnick
Keyword(s):  
Heavy Tail ◽  
Distribution Functions ◽  
Dependence Structure ◽  
Regularly Varying Functions ◽  
Exploratory Technique ◽  
The Subject ◽  
Heavy Tailed ◽  
Japanese Yen ◽  
Vague Convergence ◽  
German Mark

Univariate heavy-tailed analysis rests on the analytic notion of regularly varying functions. For multivariate heavy-tailed analysis, reliance on functions is awkward because multivariate distribution functions are not natural objects for many purposes and are difficult to manipulate. An approach based on vague convergence of measures makes the differences between univariate and multivariate analysis evaporate. We survey the foundations of the subject and discuss statistical attempts to assess dependence of large values. An exploratory technique is applied to exchange rate return data and shows clear differences in the dependence structure of large values for the Japanese Yen versus German Mark compared with the French Franc versus the German Mark.

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