Magnitude Of Violations Research Articles

Multilevel and Tail Risk Management

ABSTRACT We introduce backtesting methods to assess Value-at-Risk (VaR) and expected shortfall (ES) that require no more than desktop VaR violations as inputs. Maintaining an integrated VaR perspective, our methodology relies on multiple testing to combine evidence on the frequency and dynamic evolution of violations, and to capture more information than a single threshold can provide about the magnitude of violations. Contributions include a formal finite sample analysis of the joint distribution of multi-threshold violations, and limiting results that unify discrete and continuous definitions of cumulative violations across thresholds. Simulation studies demonstrate the power advantages of the proposed tests, particularly with small samples and when underlying models are unavailable to assessors. Results also reinforce the usefulness of CaViaR approaches not just for VaR but also as ES back-tests. Empirically, we assess desktop data by Bloomberg on exchange traded funds. We find that tail risk is not adequately reflected via a wide spectrum of models and available measures. Results provide useful prescriptions for empirical practice and, more generally, reinforce the recent arguments in favor of combined tests and forecasts in tail risk management.

Revealed Preferences over Risk and Uncertainty

We develop a nonparametric method, called Generalized Restriction of Infinite Domains (GRID), for testing the consistency of budgetary choice data with models of choice under risk and under uncertainty. Our test can allow for risk-loving and elation-seeking attitudes, or it can require risk aversion. It can also be used to calculate, via Afriat’s efficiency index, the magnitude of violations from a particular model. We evaluate the performance of various models under risk (expected utility, disappointment aversion, rank-dependent utility, and stochastically monotone utility) using data collected from several recent portfolio choice experiments. (JEL C14, D11, D12, D81)

Lower Boundary Conditions and Pricing Efficiency Testing of Indian Index Options Market : Empirical Evidence from Nifty 50 Index

This article examined the pricing efficiency of the Nifty 50 index options market by empirically testing the lower boundary conditions (LBCs), a model - free approach. The study covered a period from April 1, 2012 to March 31, 2018. The violations of LBCs indicated that options were underpriced (mispriced). The frequency and magnitude of mispriced signals were examined according to liquidity and maturity of the options contracts. This was done with the view that mere mispricing of options does not indicate inefficiency of the market. It is the opportunity to extract abnormal profit (arbitrage) from these mispriced signals which poses a serious threat to the market efficiency. It was observed that most of the mispriced signals were concentrated at the thinly traded region and options which were going to get expired. The magnitude of mispriced signals at the thinly traded region and options which were going to get expired was significantly larger than the moderately and highly traded levels and options, which were far away from the maturity date. Furthermore, in order to validate whether the differences in the magnitude of violations were statistically significant, the hypotheses were formulated and tested for both the call and put options. The results of the study suggested that the Indian index options market during the period of study was efficient as most of the mispriced signals were not exploitable due to lack of liquidity.

Modeling risk attributes of wastewater treatment plant violations of total ammonia nitrogen discharge limits in the United States

A performance-based modeling framework is developed to estimate three attributes of the risk of Total Ammonia Nitrogen (TAN) permit limit violations: probability, magnitude and frequency of violations. Discharge Monthly Report data from a sample of 106 US municipal treatment plants for the period of 2004–2008 is used for the analysis. A Generalized Linear Model regression produces estimates for the probability and frequency of TAN discharge violations, using logistic and Poisson distributions, respectively. The expected magnitude of violations is modeled as a non-stationary Generalized Pareto Distribution (GPD), using Extreme Value Theory. Regression covariates are plant inflow, fractional use of design hydraulic capacity, seasonality and previous month’s performance. The logistic regression model of the probability of a TAN violation has a median Brier Skill Score of 0.25, while the Poisson regression model of violation frequency has a median of 65% correct prediction in validation. The GPD model has equivalent model and empirical quantiles. Model predictions of probability and frequency are combined to obtain two composite risk indices—the Estimated Violation Index (EVI), which is the product of the average probabilities of violation and frequency at each location, and the Estimated Severity Index (ESI) which is the product of the EVI and the predicted 2-year return value of discharge TAN concentrations above the regulatory limit. Spatial maps of ESI and EVI provide visual guides for regulatory agencies to identify risks and prioritize compliance and enforcement efforts.

Risk models-at-risk

The experience from the global financial crisis has raised serious concerns about the accuracy of standard risk measures as tools for the quantification of extreme downward risks. A key reason for this is that risk measures are subject to a model risk due, e.g. to specification and estimation uncertainty. While regulators have proposed that financial institutions assess the model risk, there is no accepted approach for computing such a risk. We propose a remedy for this by a general framework for the computation of risk measures robust to model risk by empirically adjusting the imperfect risk forecasts by outcomes from backtesting frameworks, considering the desirable quality of VaR models such as the frequency, independence and magnitude of violations. We also provide a fair comparison between the main risk models using the same metric that corresponds to model risk required corrections.

An Economic Evaluation of the Model Risk for Risk Models

The recent experience from the global financial crisis has raised serious doubts about the accuracy of standard risk measures as a tool to quantify extreme downward risks. Standard risk measures are subject to a “model risk” due to the specification and estimation uncertainty. We propose a general adjustment of the Value-at-Risk to compute risk measures robust to the model risk. The proposed procedure aims empirically adjusting the imperfect quantile estimate assessing the good quality of VaR models such as frequency exceptions, independence of violations and magnitude of violations. Based on a long sample of U.S. data, we find an inverse U-shape relation between VaR model errors and the horizon: corrections (for model errors) are higher for short-term horizons but are also increasing for long-term horizons. We also provide a fair comparison between the main risk models using the same metric that corresponds to model risk required corrections.