A New Family of Heavy Tailed Symmetric Distribution for Modeling Financial Data

2017 ◽  
Vol 6 (3) ◽  
pp. 577-586 ◽  
Author(s):  
Nitha K. U. ◽  
Krishnarani S. D.
Keyword(s):  
Financial Data ◽  
Symmetric Distribution ◽  
New Family ◽  
Heavy Tailed

scholarly journals A New Class of Heavy-Tailed Distributions: Modeling and Simulating Actuarial Measures

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Jin Zhao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
E. H. Hafez ◽  
Marwa M. Mohie El-Din
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Weibull Model ◽  
Financial Data ◽  
Statistical Distributions ◽  
New Family ◽  
Heavy Tailed Distributions ◽  
Beta Power ◽  
Heavy Tailed ◽  
Modeling Data

Statistical distributions play a prominent role for modeling data in applied fields, particularly in actuarial, financial sciences, and risk management fields. Among the statistical distributions, the heavy-tailed distributions have proven the best choice to use for modeling heavy-tailed financial data. The actuaries are often in search of such types of distributions to provide the best description of the actuarial and financial data. This study presents a new power transformation to introduce a new family of heavy-tailed distributions useful for modeling heavy-tailed financial data. A submodel, namely, heavy-tailed beta-power transformed Weibull model is considered to demonstrate the adequacy of the proposed method. Some actuarial measures such as value at risk, tail value at risk, tail variance, and tail variance premium are calculated. A brief simulation study based on these measures is provided. Finally, an application to the insurance loss dataset is analyzed, which revealed that the proposed distribution is a superior model among the competitors and could potentially be very adequate in describing and modeling actuarial and financial data.

Asymmetric heavy-tailed vector auto-regressive processes with application to financial data

2019 ◽  
Vol 90 (2) ◽  
pp. 324-340 ◽  
Author(s):  
Mohsen Maleki ◽  
Darren Wraith ◽  
Mohammad R. Mahmoudi ◽  
Javier E. Contreras-Reyes
Keyword(s):  
Financial Data ◽  
Auto Regressive ◽  
Heavy Tailed

scholarly journals The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*

2019 ◽  
Vol 18 (2) ◽  
pp. 395-424 ◽  
Author(s):  
Yuzhi Cai ◽  
Julian Stander
Keyword(s):  
Value At Risk ◽  
Empirical Work ◽  
Garch Model ◽  
Likelihood Estimation ◽  
Threshold Value ◽  
Financial Data ◽  
Financial Returns ◽  
Density Forecasting ◽  
Heavy Tailed ◽  
Density Forecasts

AbstractWe consider multiple threshold value-at-risk (VaRt) estimation and density forecasting for financial data following a threshold GARCH model. We develop an α-quantile quasi-maximum likelihood estimation (QMLE) method for VaRt by showing that the associated density function is an α-quantile density and belongs to the tick-exponential family. This establishes that our estimator is consistent for the parameters of VaRt. We propose a density forecasting method for quantile models based on VaRt at a single nonextreme level, which overcomes some limitations of existing forecasting methods with quantile models. We find that for heavy-tailed financial data our α-quantile QMLE method for VaRt outperforms the Gaussian QMLE method for volatility. We also find that density forecasts based on VaRt outperform those based on the volatility of financial data. Empirical work on market returns shows that our approach also outperforms some benchmark models for density forecasting of financial returns.

A Student t-mixture autoregressive model with applications to heavy-tailed financial data

Biometrika ◽  
2009 ◽  
Vol 96 (3) ◽  
pp. 751-760 ◽  
Author(s):  
C. S. Wong ◽  
W. S. Chan ◽  
P. L. Kam
Keyword(s):  
Autoregressive Model ◽  
Financial Data ◽  
Heavy Tailed

scholarly journals Assessing The Relative Performance Of Heavy-Tailed Distributions: Empirical Evidence From The Johannesburg Stock Exchange

2014 ◽  
Vol 30 (4) ◽  
pp. 1263 ◽  
Author(s):  
Chun-Sung Huang ◽  
Chun-Kai Huang ◽  
Knowledge Chinhamu
Keyword(s):  
Risk Management ◽  
Value At Risk ◽  
Goodness Of Fit ◽  
Empirical Distribution ◽  
Stock Exchange ◽  
Vital Role ◽  
Financial Data ◽  
Johannesburg Stock Exchange ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed

<p>It has been well documented that the empirical distribution of daily logarithmic returns from financial market variables is characterized by excess kurtosis and skewness. In order to capture such properties in financial data, heavy-tailed and asymmetric distributions are required to overcome shortfalls of the widely exhausted classical normality assumption. In the context of financial forecasting and risk management, the accuracy in modeling the underlying returns distribution plays a vital role. For example, risk management tools such as value-at-risk (VaR) are highly dependent on the underlying distributional assumption, with particular focus being placed at the extreme tails. Hence, identifying a distribution that best captures all aspects of the given financial data may provide vast advantages to both investors and risk managers. In this paper, we investigate major financial indices on the Johannesburg Stock Exchange (JSE) and fit their associated returns to classes of heavy tailed distributions. The relative adequacy and goodness-of-fit of these distributions are then assessed through the robustness of their respective VaR estimates. Our results indicate that the best model selection is not only variant across the indices, but also across different VaR levels and the dissimilar tails of return series.</p>

scholarly journals A Doubling Method for the Generalized Lambda Distribution

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Todd C. Headrick ◽  
Mohan D. Pant
Keyword(s):  
Monte Carlo ◽  
Pearson Correlation ◽  
Relative Bias ◽  
Simulation Studies ◽  
Generalized Lambda Distribution ◽  
New Family ◽  
Heavy Tailed Distributions ◽  
Moment Estimates ◽  
Doubling Method ◽  
Heavy Tailed

This paper introduces a new family of generalized lambda distributions (GLDs) based on a method of doubling symmetric GLDs. The focus of the development is in the context of L-moments and L-correlation theory. As such, included is the development of a procedure for specifying double GLDs with controlled degrees of L-skew, L-kurtosis, and L-correlations. The procedure can be applied in a variety of settings such as modeling events and Monte Carlo or simulation studies. Further, it is demonstrated that estimates of L-skew, L-kurtosis, and L-correlation are substantially superior to conventional product-moment estimates of skew, kurtosis, and Pearson correlation in terms of both relative bias and efficiency when heavy tailed distributions are of concern.

scholarly journals A Toolkit for Robust Risk Assessment Using F-Divergences

2021 ◽  
Author(s):  
Thomas Kruse ◽  
Judith C. Schneider ◽  
Nikolaus Schweizer
Keyword(s):  
Operations Management ◽  
Reference Model ◽  
Model Risk ◽  
Worst Case ◽  
Reference Models ◽  
New Family ◽  
Uncertainty Sets ◽  
Open Source Software Package ◽  
Heavy Tailed ◽  
Theoretical Results

This paper assembles a toolkit for the assessment of model risk when model uncertainty sets are defined in terms of an F-divergence ball around a reference model. We propose a new family of F-divergences that are easy to implement and flexible enough to imply convincing uncertainty sets for broad classes of reference models. We use our theoretical results to construct concrete examples of divergences that allow for significant amounts of uncertainty about lognormal or heavy-tailed Weibull reference models without implying that the worst case is necessarily infinitely bad. We implement our tools in an open-source software package and apply them to three risk management problems from operations management, insurance, and finance. This paper was accepted by Baris Ata, stochastic models and simulation.

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