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.

scholarly journals MULTIVARIATE HEAVY-TAILED MODELS FOR VALUE-AT-RISK ESTIMATION

2012 ◽  
Vol 15 (04) ◽  
pp. 1250029 ◽  
Author(s):  
CARLO MARINELLI ◽  
STEFANO D'ADDONA ◽  
SVETLOZAR T. RACHEV
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Stock Price ◽  
Risk Estimation ◽  
Price Data ◽  
Heavy Tailed Distributions ◽  
Derivative Instruments ◽  
Heavy Tailed ◽  
Student’S T

For purposes of Value-at-Risk estimation, we consider several multivariate families of heavy-tailed distributions, which can be seen as multidimensional versions of Paretian stable and Student's t distributions allowing different marginals to have different indices of tail thickness. After a discussion of relevant estimation and simulation issues, we conduct a backtesting study on a set of portfolios containing derivative instruments, using historical US stock price data.

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 On Modeling the Earthquake Insurance Data via a New Member of the T-X Family

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
Omid Kharazmi
Keyword(s):  
At Risk ◽  
Maximum Likelihood ◽  
Simulation Study ◽  
Value At Risk ◽  
Model Parameters ◽  
Earthquake Insurance ◽  
Monte Carlo Simulation Study ◽  
Heavy Tailed ◽  
Modeling Data ◽  
Insurance Data

Heavy-tailed distributions play an important role in modeling data in actuarial and financial sciences. In this article, a new method is suggested to define new distributions suitable for modeling data with a heavy right tail. The proposed method may be named as the Z-family of distributions. For illustrative purposes, a special submodel of the proposed family, called the Z-Weibull distribution, is considered in detail to model data with a heavy right tail. The method of maximum likelihood estimation is adopted to estimate the model parameters. A brief Monte Carlo simulation study for evaluating the maximum likelihood estimators is done. Furthermore, some actuarial measures such as value at risk and tail value at risk are calculated. A simulation study based on these actuarial measures is also done. An application of the Z-Weibull model to the earthquake insurance data is presented. Based on the analyses, we observed that the proposed distribution can be used quite effectively in modeling heavy-tailed data in insurance sciences and other related fields. Finally, Bayesian analysis and performance of Gibbs sampling for the earthquake data have also been carried out.

scholarly journals Value at Risk estimation using GAS models with heavy tailed distributions for cryptocurrencies

2021 ◽  
Vol 10 (4) ◽  
pp. 40-54
Author(s):  
Stephanie Danielle Subramoney ◽  
Knowledge Chinhamu ◽  
Retius Chifurira
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Estimation ◽  
Ratio Test ◽  
Student’S T Distribution ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
Student’S T ◽  
Student's T Distribution ◽  
T Distribution

  Risk management and prediction of market losses of cryptocurrencies are of notable value to risk managers, portfolio managers, financial market researchers and academics. One of the most common measures of an asset’s risk is Value-at-Risk (VaR). This paper evaluates and compares the performance of generalized autoregressive score (GAS) combined with heavy-tailed distributions, in estimating the VaR of two well-known cryptocurrencies’ returns, namely Bitcoin returns and Ethereum returns. In this paper, we proposed a VaR model for Bitcoin and Ethereum returns, namely the GAS model combined with the generalized lambda distribution (GLD), referred to as the GAS-GLD model. The relative performance of the GAS-GLD models was compared to the models proposed by Troster et al. (2018), in other words, GAS models combined with asymmetric Laplace distribution (ALD), the asymmetric Student’s t-distribution (AST) and the skew Student’s t-distribution (SSTD). The Kupiec likelihood ratio test was used to assess the adequacy of the proposed models. The principal findings suggest that the GAS models with heavy-tailed innovation distributions are, in fact, appropriate for modelling cryptocurrency returns, with the GAS-GLD being the most adequate for the Bitcoin returns at various VaR levels, and both GAS-SSTD, GAS-ALD and GAS-GLD models being the most appropriate for the Ethereum returns at the VaR levels used in this study.    

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.

Efficient Computation of Value at Risk with Heavy-Tailed Risk Factors

2009 ◽  
Author(s):  
Cheng-der Fuh ◽  
Inchi Hu ◽  
Kate Hsu ◽  
Ren-Her Wang
Keyword(s):  
Risk Factors ◽  
At Risk ◽  
Value At Risk ◽  
Efficient Computation ◽  
Heavy Tailed

scholarly journals Multivariate Heavy-Tailed Models for Value-at-Risk Estimation

2011 ◽  
Author(s):  
Carlo Marinelli ◽  
Stefano d'Addona ◽  
Svetlozar Rachev
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Estimation ◽  
Heavy Tailed
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