Limit Theory for Forecasts of Extreme Distortion Risk Measures and Expectiles*

2019 ◽  
Author(s):  
Yannick Hoga
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Limit Theory ◽  
Extreme Risk ◽  
Wide Range ◽  
Scale Models ◽  
Adequate Coverage ◽  
Nonparametric Alternatives ◽  
Do So ◽  
Distortion Risk Measures

Abstract We develop central limit theory for tail risk forecasts in general location–scale models. We do so for a wide range of risk measures, viz. distortion risk measures (DRMs) and expectiles. Two popular members of the class of DRMs are the Value-at-Risk and the Expected Shortfall. The forecasts we consider are motivated by a Pareto-type tail assumption for the innovations and allow for extrapolation beyond the range of available observations. Simulations reveal adequate coverage of the forecast intervals derived from the limit theory. An empirical application demonstrates that our estimators outperform nonparametric alternatives when forecasting extreme risk in sufficiently large samples.

Extreme Conditional Tail Moment Estimation under Serial Dependence

2018 ◽  
Vol 17 (4) ◽  
pp. 587-615 ◽  
Author(s):  
Yannick Hoga
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Simultaneous Inference ◽  
Serial Dependence ◽  
Absolute Deviation ◽  
Limit Theory ◽  
Risk Levels ◽  
Moment Estimation ◽  
Wide Range ◽  
Dependence Assumption

Abstract A wide range of risk measures can be written as functions of conditional tail moments (CTMs) and value-at-risk (VaR), for instance the expected shortfall (ES). In this paper, we derive joint central limit theory for semi-parametric estimates of CTMs, including in particular ES, at arbitrarily small risk levels. We also derive confidence corridors for VaR at different levels far out in the tail, which allows for simultaneous inference. We work under a semi-parametric Pareto-type assumption on the distributional tail of the observations and only require an extremal-near epoch dependence assumption on the serial dependence. In simulations, our semi-parametric ES estimate is often shown to be more accurate in terms of mean absolute deviation than extant non- and semi-parametric estimates. An empirical application to the extreme swings in Volkswagen log-returns during the failed takeover attempt by Porsche illustrates the proposed methods.

SET-VALUED LAW INVARIANT COHERENT AND CONVEX RISK MEASURES

2019 ◽  
Vol 22 (03) ◽  
pp. 1950004 ◽  
Author(s):  
YANHONG CHEN ◽  
YIJUN HU
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Convex Risk Measures ◽  
New Class ◽  
The Relationship ◽  
Distortion Risk Measures

In this paper, we investigate representation results for set-valued law invariant coherent and convex risk measures, which can be considered as a set-valued extension of the multivariate scalar law invariant coherent and convex risk measures studied in the literature. We further introduce a new class of set-valued risk measures, named set-valued distortion risk measures, which can be considered as a set-valued version of multivariate scalar distortion risk measures introduced in the literature. The relationship between set-valued distortion risk measures and set-valued weighted value at risk is also given.

ASYMPTOTIC EXPANSIONS OF GENERALIZED QUANTILES AND EXPECTILES FOR EXTREME RISKS

2015 ◽  
Vol 29 (3) ◽  
pp. 309-327 ◽  
Author(s):  
Tiantian Mao ◽  
Kai Wang Ng ◽  
Taizhong Hu
Keyword(s):  
Value At Risk ◽  
Risk Measures ◽  
Domain Of Attraction ◽  
Random Variable ◽  
Second Order ◽  
Underlying Distribution ◽  
First Order ◽  
Extreme Risk ◽  
Special Cases ◽  
Extreme Risks

Generalized quantiles of a random variable were defined as the minimizers of a general asymmetric loss function, which include quantiles, expectiles and M-quantiles as their special cases. Expectiles have been suggested as potentially better alternatives to both Value-at-Risk and expected shortfall risk measures. In this paper, we first establish the first-order expansions of generalized quantiles for extreme risks as the confidence level α↑ 1, and then investigate the first-order and/or second-order expansions of expectiles of an extreme risk as α↑ 1 according to the underlying distribution belonging to the max-domain of attraction of the Fréchet, Weibull, and Gumbel distributions, respectively. Examples are also presented to examine whether and how much the first-order expansions have been improved by the second-order expansions.

scholarly journals Beyond Value-at-Risk: GlueVaR Distortion Risk Measures

Risk Analysis ◽  
2013 ◽  
Vol 34 (1) ◽  
pp. 121-134 ◽  
Author(s):  
Jaume Belles-Sampera ◽  
Montserrat Guillén ◽  
Miguel Santolino
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Distortion Risk Measures

Risk Measurement and Management for Hedge Funds

2017 ◽  
Author(s):  
Guillaume Weisang
Keyword(s):  
Hedge Funds ◽  
Value At Risk ◽  
Risk Measures ◽  
Hedge Fund ◽  
Risk Measurement ◽  
Tail Risk ◽  
Equity Risk ◽  
Wide Range ◽  
Measurement Tools ◽  
Hedge Fund Risk

Risk measurement and management is an important and complex subject for hedge fund stakeholders, managers, and investors. Given that hedge funds dynamically trade a wide range of financial instruments, their returns show tail risk and nonlinear characteristics with respect to many financial markets that require advanced downside risk measures, such as value-at-risk, expected shortfall, and tail risk, to capture risk adequately. This chapter reviews the nature of these risks and presents the measurement tools needed, focusing on fixed-income instruments, derivative securities, and equity risk measurement, and stressing the importance of frequent assessment to capture the possibly rapidly changing risk profiles of hedge funds. This chapter also provides an overview of the linear factor models that investors often use to measure hedge fund risk exposures along many risk factors.

OPTIMAL REINSURANCE DESIGN WITH DISTORTION RISK MEASURES AND ASYMMETRIC INFORMATION

2021 ◽  
pp. 1-23
Author(s):  
Tim J. Boonen ◽  
Yiying Zhang
Keyword(s):  
At Risk ◽  
Asymmetric Information ◽  
Value At Risk ◽  
Functional Form ◽  
Risk Measures ◽  
Risk Measure ◽  
Incentive Compatibility ◽  
Optimal Reinsurance ◽  
Net Profit ◽  
Distortion Risk Measures

ABSTRACT This paper studies a problem of optimal reinsurance design under asymmetric information. The insurer adopts distortion risk measures to quantify his/her risk position, and the reinsurer does not know the functional form of this distortion risk measure. The risk-neutral reinsurer maximizes his/her net profit subject to individual rationality and incentive compatibility constraints. The optimal reinsurance menu is succinctly derived under the assumption that one type of insurer has a larger willingness to pay than the other type of insurer for every risk. Some comparative analyses are given as illustrations when the insurer adopts the value at risk or the tail value at risk as preferences.

scholarly journals Extreme Risk, Value-At-Risk And Expected Shortfall In The Gold Market

2014 ◽  
Vol 14 (1) ◽  
pp. 107
Author(s):  
Knowledge Chinhamu ◽  
Chun-Kai Huang ◽  
Chun-Sung Huang ◽  
Delson Chikobvu
Keyword(s):  
At Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Effective Means ◽  
Value Theory ◽  
Expected Shortfall ◽  
Extreme Stress ◽  
Extreme Risk ◽  
Gold Market ◽  
The Impact

Extreme value theory (EVT) has been widely applied in fields such as hydrology and insurance. It is a tool used to reflect on probabilities associated with extreme, and thus rare, events. EVT is useful in modeling the impact of crashes or situations of extreme stress on investor portfolios. It describes the behavior of maxima or minima in a time series, i.e., tails of a distribution. In this paper, we propose the use of generalised Pareto distribution (GPD) to model extreme returns in the gold market. This method provides effective means of estimating tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES). This is confirmed by various backtesting procedures. In particular, we utilize the Kupiec unconditional coverage test and the Christoffersen conditional coverage test for VaR backtesting, while the Bootstrap test is used for ES backtesting. The results indicate that GPD is superior to the traditional Gaussian and Students t models for VaR and ES estimations.

Equivalent Distortion Risk Measures on Moment Spaces

2018 ◽  
Author(s):  
Dries Cornilly ◽  
Steven Vanduffel
Keyword(s):  
Risk Measures ◽  
Moment Spaces ◽  
Distortion Risk Measures

scholarly journals Early warning of systemic risk in global banking: eigen-pair R number for financial contagion and market price-based methods

2021 ◽  
Author(s):  
Sheri Markose ◽  
Simone Giansante ◽  
Nicolas A. Eterovic ◽  
Mateusz Gatkowski
Keyword(s):  
Early Warning ◽  
Systemic Risk ◽  
Value At Risk ◽  
Risk Measures ◽  
Market Price ◽  
System Stability ◽  
Conditional Value At Risk ◽  
Centrality Measures ◽  
Global Banking ◽  
Pair Method

AbstractWe analyse systemic risk in the core global banking system using a new network-based spectral eigen-pair method, which treats network failure as a dynamical system stability problem. This is compared with market price-based Systemic Risk Indexes, viz. Marginal Expected Shortfall, Delta Conditional Value-at-Risk, and Conditional Capital Shortfall Measure of Systemic Risk in a cross-border setting. Unlike paradoxical market price based risk measures, which underestimate risk during periods of asset price booms, the eigen-pair method based on bilateral balance sheet data gives early-warning of instability in terms of the tipping point that is analogous to the R number in epidemic models. For this regulatory capital thresholds are used. Furthermore, network centrality measures identify systemically important and vulnerable banking systems. Market price-based SRIs are contemporaneous with the crisis and they are found to covary with risk measures like VaR and betas.

scholarly journals Towards Reduced CNNs for De-Noising Phase Images Corrupted with Speckle Noise

Photonics ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 255
Author(s):  
Marie Tahon ◽  
Silvio Montresor ◽  
Pascal Picart
Keyword(s):  
Phase Error ◽  
Speckle Noise ◽  
Experimental Conditions ◽  
Benchmark Data ◽  
Wide Range ◽  
Phase Images ◽  
Different Depths ◽  
Phase Data ◽  
Do So

Digital holography is a very efficient technique for 3D imaging and the characterization of changes at the surfaces of objects. However, during the process of holographic interferometry, the reconstructed phase images suffer from speckle noise. In this paper, de-noising is addressed with phase images corrupted with speckle noise. To do so, DnCNN residual networks with different depths were built and trained with various holographic noisy phase data. The possibility of using a network pre-trained on natural images with Gaussian noise is also investigated. All models are evaluated in terms of phase error with HOLODEEP benchmark data and with three unseen images corresponding to different experimental conditions. The best results are obtained using a network with only four convolutional blocks and trained with a wide range of noisy phase patterns.

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