scholarly journals A consistent estimator to the orthant-based tail value-at-risk

2018 ◽  
Vol 22 ◽  
pp. 163-177 ◽  
Author(s):  
Nicholas Beck ◽  
Mélina Mailhot
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Arbitrary Dimension ◽  
Real Data ◽  
Consistent Estimator ◽  
Numerical Examples ◽  
Theoretical Results

In this paper, we address the estimation of multivariate value-at-risk (VaR) and tail value-at-risk (TVaR). We recall definitions for the bivariate lower and upper orthant VaR and bivariate lower and upper orthant TVaR, presented in Cossette et al. [Eur. Actuar. J. 3 (2013) 321–357 or Methodol. Comput. Appl. Probab. (2014) 1–22]. Here, we present estimators for both these measures extended to an arbitrary dimension d ≥ 2 and establish the consistency of our estimator for the lower and upper orthant TVaR in any dimension. We demonstrate these results by providing numerical examples that compare our estimator to theoretical results for both simulated and real data.

scholarly journals Optimal reinsurance: a reinsurer’s perspective

2017 ◽  
Vol 12 (1) ◽  
pp. 147-184 ◽  
Author(s):  
Fei Huang ◽  
Honglin Yu
Keyword(s):  
At Risk ◽  
Closed Form ◽  
Value At Risk ◽  
Optimality Criteria ◽  
Total Loss ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Dependency Structure ◽  
Closed Form Solutions

AbstractIn this paper, the optimal safety loading that the reinsurer should set in the reinsurance pricing is studied, which is novel in the literature. It is first assumed that the insurer will choose the form of the reinsurance contract by following the results derived in Cai et al. Different optimality criteria from the reinsurer’s perspective are then studied, such as maximising the expectation of the profit, maximising the utility of the profit and minimising the value-at-risk of the reinsurer’s total loss. By applying the concept of comonotonicity, the problem in which the reinsurer is facing two risks with unknown dependency structure is also solved. Closed-form solutions are obtained when the underlying losses are zero-modified exponentially distributed. Finally, numerical examples are provided to illustrate the results derived.

scholarly journals Optimal Limited Stop-Loss Reinsurance under VaR, TVaR, and CTE Risk Measures

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Xianhua Zhou ◽  
Huadong Zhang ◽  
Qingquan Fan
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Loss Ratio ◽  
Optimal Reinsurance ◽  
Numerical Examples ◽  
Optimal Values ◽  
Stop Loss ◽  
Conditional Tail Expectation ◽  
Reinsurance Market

This paper aims to provide a practical optimal reinsurance scheme under particular conditions, with the goal of minimizing total insurer risk. Excess of loss reinsurance is an essential part of the reinsurance market, but the concept of stop-loss reinsurance tends to be unpopular. We study the purchase arrangement of optimal reinsurance, under which the liability of reinsurers is limited by the excess of loss ratio, in order to generate a reinsurance scheme that is closer to reality. We explore the optimization of limited stop-loss reinsurance under three risk measures: value at risk (VaR), tail value at risk (TVaR), and conditional tail expectation (CTE). We analyze the topic from the following aspects: (1) finding the optimal franchise point with limited stop-loss coverage, (2) finding the optimal limited stop-loss coverage within a certain franchise point, and (3) finding the optimal franchise point with limited stop-loss coverage. We provide several numerical examples. Our results show the existence of optimal values and locations under the various constraint conditions.

scholarly journals Dynamic D-Vine Copula Model with Applications to Value-at-Risk (VaR)

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Paula V. Tófoli ◽  
Flávio A. Ziegelmann ◽  
Osvaldo Candido ◽  
Pedro L. Valls Pereira
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Predictive Accuracy ◽  
Sharp Decrease ◽  
Real Data ◽  
The United States ◽  
Financial Return ◽  
Vine Copula ◽  
Market Indexes ◽  
In The Beginning

Abstract Vine copulas are multivariate dependence models constructed from pair-copulas (bivariate copulas). In this paper, we allow the dependence parameters of the pair-copulas in a D-vine decomposition to be potentially time-varying, following a restricted ARMA(1, m) process, in order to obtain a very flexible dependence model for applications to multivariate financial return data. We investigate the dependence among the broad stock market indexes from Germany (DAX), France (CAC 40), Britain (FTSE 100), the United States (S&P 500) and Brazil (IBOVESPA) both in a crisis and in a non-crisis period. We find evidence of stronger dependence among the indexes in bear markets. Surprisingly, though, the dynamic D-vine copula indicates the occurrence of a sharp decrease in dependence between the indexes FTSE and CAC in the beginning of 2011, and also between CAC and DAX during mid-2011 and in the beginning of 2008, suggesting the absence of contagion in these cases. We evaluate the dynamic D-vine copula with respect to Value-at-Risk (VaR) forecasting accuracy in crisis periods. The dynamic D-vine outperforms the static D-vine in terms of predictive accuracy for our real data sets. We also investigate the dynamic D-vine copula in a simulation study and the overall results of the Monte Carlo experiments are quite favorable to the dynamic D-vine copula in comparison with a static D-vine copula.

Risk Asset Portfolio Choice Models under Three Risk Measures

2011 ◽  
Vol 204-210 ◽  
pp. 537-540
Author(s):  
Yu Ling Wang ◽  
Jun Hai Ma ◽  
Yu Hua Xu
Keyword(s):  
At Risk ◽  
Portfolio Choice ◽  
Value At Risk ◽  
Financial Risk ◽  
Risk Measures ◽  
Empirical Support ◽  
Real Data ◽  
Conditional Value At Risk ◽  
Asset Portfolio ◽  
Special Value

Mean-variance model, value at risk and Conditional Value at Risk are three chief methods to measure financial risk recently. The demonstrative research shows that three optional questions are equivalence when the security rates have a multivariate normal distribution and the given confidence level is more than a special value. Applications to real data provide empirical support to this methodology. This result has provided new methods for us about further research of risk portfolios.

scholarly journals On Partial Stochastic Comparisons Based on Tail Values at Risk

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1181
Author(s):  
Alfonso J. Bello ◽  
Julio Mulero ◽  
Miguel A. Sordo ◽  
Alfonso Suárez-Llorens
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measure ◽  
Real Data ◽  
Stochastic Orders ◽  
Stochastic Comparisons ◽  
Increasing Convex Order ◽  
Asset Return ◽  
Confidence Levels ◽  
Return Distributions

The tail value at risk at level p, with p ∈ ( 0 , 1 ) , is a risk measure that captures the tail risk of losses and asset return distributions beyond the p quantile. Given two distributions, it can be used to decide which is riskier. When the tail values at risk of both distributions agree, whenever the probability level p ∈ ( 0 , 1 ) , about which of them is riskier, then the distributions are ordered in terms of the increasing convex order. The price to pay for such a unanimous agreement is that it is possible that two distributions cannot be compared despite our intuition that one is less risky than the other. In this paper, we introduce a family of stochastic orders, indexed by confidence levels p 0 ∈ ( 0 , 1 ) , that require agreement of tail values at risk only for levels p > p 0 . We study its main properties and compare it with other families of stochastic orders that have been proposed in the literature to compare tail risks. We illustrate the results with a real data example.

scholarly journals Heavy-Tailed Log-Logistic Distribution: Properties, Risk Measures and Applications

2021 ◽  
Vol 9 (4) ◽  
pp. 910-941
Author(s):  
Abd-Elmonem A. M. Teamah ◽  
Ahmed A. Elbanna ◽  
Ahmed M. Gemeay
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Real Data ◽  
Estimation Methods ◽  
Logistic Distribution ◽  
Model Parameters ◽  
Data Sets ◽  
Alpha Power ◽  
Heavy Tailed

Heavy tailed distributions have a big role in studying risk data sets. Statisticians in many cases search and try to find new or relatively new statistical models to fit data sets in different fields. This article introduced a relatively new heavy-tailed statistical model by using alpha power transformation and exponentiated log-logistic distribution which called alpha power exponentiated log-logistic distribution. Its statistical properties were derived mathematically such as moments, moment generating function, quantile function, entropy, inequality curves and order statistics. Five estimation methods were introduced mathematically and the behaviour of the proposed model parameters was checked by randomly generated data sets and these estimation methods. Also, some actuarial measures were deduced mathematically such as value at risk, tail value at risk, tail variance and tail variance premium. Numerical values for these measures were performed and proved that the proposed distribution has a heavier tail than others compared models. Finally, three real data sets from different fields were used to show how these proposed models fitting these data sets than other many wells known and related models.

scholarly journals Estimação Local de Valor em Risco Baseado em Cópulas

2009 ◽  
Vol 7 (1) ◽  
pp. 29
Author(s):  
Eduardo F. L. De Melo ◽  
Beatriz Vaz de Melo Mendes
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Estimation ◽  
Asymptotic Variance ◽  
Local Maximum ◽  
Real Data ◽  
Likelihood Method ◽  
Out Of Sample ◽  
Local Maximum Likelihood ◽  
Individual Asset

In this paper we propose the local maximum likelihood method for dynamically estimate copula parameters. We study the estimates statistical properties and derive the expression for their asymptotic variance in the case of Gaussian copulas. The local estimates are able to detect temporal changes in the strength of dependence among assets. These dynamics are combined with a GARCH type modeling of each individual asset to estimate the Value- at-Risk. The performance of the proposed estimates is investigated through Monte Carlo simulation experiments. In an application using real data, an out-of-sample test indicated that the new methodology may outperform the constant copula model when it comes to Value-at-Risk estimation.

scholarly journals Value at Risk Based on Fuzzy Numbers

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 98
Author(s):  
Maria Letizia Guerra ◽  
Laerte Sorini
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Fuzzy Numbers ◽  
Real Data ◽  
Quantile Function ◽  
Fixed Time ◽  
Testing Procedure ◽  
Historical Simulation ◽  
Modelling Uncertainty ◽  
Cumulative Function

Value at Risk (VaR) has become a crucial measure for decision making in risk management over the last thirty years and many estimation methodologies address the finding of the best performing measure at taking into account unremovable uncertainty of real financial markets. One possible and promising way to include uncertainty is to refer to the mathematics of fuzzy numbers and to its rigorous methodologies which offer flexible ways to read and to interpret properties of real data which may arise in many areas. The paper aims to show the effectiveness of two distinguished models to account for uncertainty in VaR computation; initially, following a non parametric approach, we apply the Fuzzy-transform approximation function to smooth data by capturing fundamental patterns before computing VaR. As a second model, we apply the Average Cumulative Function (ACF) to deduce the quantile function at point p as the potential loss VaRp for a fixed time horizon for the 100p% of the values. In both cases a comparison is conducted with respect to the identification of VaR through historical simulation: twelve years of daily S&P500 index returns are considered and a back testing procedure is applied to verify the number of bad VaR forecasting in each methodology. Despite the preliminary nature of the research, we point out that VaR estimation, when modelling uncertainty through fuzzy numbers, outperforms the traditional VaR in the sense that it is the closest to the right amount of capital to allocate in order to cover future losses in normal market conditions.

Single-Index Expectile Models for Estimating Conditional Value at Risk and Expected Shortfall*

2020 ◽  
Author(s):  
Rong Jiang ◽  
Xueping Hu ◽  
Keming Yu
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Real Data ◽  
Expected Shortfall ◽  
Conditional Value At Risk ◽  
Finite Sample ◽  
Single Index ◽  
Index Model ◽  
Index Approach ◽  
The One

Abstract This article develops a single-index approach for modeling the expectile-based value at risk (EVaR). EVaR has an advantage over the conventional quantile-based VaR (QVaR) of being more sensitive to the magnitude of extreme losses. EVaR can also be used for calculating QVaR and expected shortfall (ES) by exploiting the one-to-one mapping from expectiles to quantiles and the relationship between VaR and ES. We develop an asymmetric least squares technique for estimating the unknown regression parameter and link function in a single-index model, and establish the asymptotic normality of the resultant estimators. Simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods.

scholarly journals A GARCH APPROACH TO VaR CALCULATION IN FINANCIAL MARKET

2020 ◽  
Vol 1 (1) ◽  
pp. 35-46
Author(s):  
Nurfadhlina Abdul Halim ◽  
Endang Soeryana ◽  
Alit Kartiwa
Keyword(s):  
At Risk ◽  
Financial Market ◽  
Value At Risk ◽  
Time Horizon ◽  
Financial Institution ◽  
Garch Model ◽  
Real Data ◽  
Standard Measurement

Value at Risk (VaR) has already becomes a standard measurement that must be carried out by financial institution for both internal interest and regulatory. VaR is defined as the value that portfolio will loss with a certain probability value and over a certain time horizon (usually one or ten days). In this paper we examine of VaR calculation when the volatility is not constant using generalized autoregressive conditional heteroscedastic (GARCH) model. We illustrate the method to real data from Indonesian financial market that is the stock of PT. Indosat Tbk.

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