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1.
Value at Risk has lost the battle against Expected Shortfall on theoretical grounds, the latter satisfying all coherence properties while the former may, on carefully constructed cases, lack the sub-additivity property that is in a sense, the most important property a risk measure ought to satisfy. While the superiority of Expected Shortfall is evident as a theoretical tool, little has been researched on the properties of estimators proposed in the literature. Since those estimators are the real tools for calculating bank capital reserves in practice, the natural question that one may ask is whether a given estimator of Expected Shortfall also satisfies the coherence properties. In this paper, we show that it is possible to have estimators of Expected Shortfall that do not satisfy the sub-additivity condition. This finding should motivate risk managers and quantitative asset managers to investigate further the properties of the estimators of the risk measures they are currently utilizing. 相似文献
2.
Paralleling regulatory developments, we devise value-at-risk and expected shortfall type risk measures for the potential losses arising from using misspecified models when pricing and hedging contingent claims. Essentially, P&L from model risk corresponds to P&L realized on a perfectly hedged position. Model uncertainty is expressed by a set of pricing models, each of which represents alternative asset price dynamics to the model used for pricing. P&L from model risk is determined relative to each of these models. Using market data, a unified loss distribution is attained by weighing models according to a likelihood criterion involving both calibration quality and model parsimony. Examples demonstrate the magnitude of model risk and corresponding capital buffers necessary to sufficiently protect trading book positions against unexpected losses from model risk. A further application of the model risk framework demonstrates the calculation of gap risk of a barrier option when employing a semi-static hedging strategy. 相似文献
3.
This paper demonstrates that existing quantile regression models used for jointly forecasting Value-at-Risk (VaR) and expected shortfall (ES) are sensitive to initial conditions. Given the importance of these measures in financial systems, this sensitivity is a critical issue. A new Bayesian quantile regression approach is proposed for estimating joint VaR and ES models. By treating the initial values as unknown parameters, sensitivity issues can be dealt with. Furthermore, new additive-type models are developed for the ES component that are more robust to initial conditions. A novel approach using the open-faced sandwich (OFS) method is proposed which improves uncertainty quantification in risk forecasts. Simulation and empirical results highlight the improvements in risk forecasts ensuing from the proposed methods. 相似文献
4.
(G)ARCH-type models are frequently used for the dynamic modelling and forecasting of risk attached to speculative asset returns. While the symmetric and conditionally Gaussian GARCH model has been generalized in a manifold of directions, model innovations are mostly presumed to stem from an underlying IID distribution. For a cross section of 18 stock market indices, we notice that (threshold) (T)GARCH-implied model innovations are likely at odds with the commonly held IID assumption. Two complementary strategies are pursued to evaluate the conditional distributions of consecutive TGARCH innovations, a non-parametric approach and a class of standardized copula distributions. Modelling higher order dependence patterns is found to improve standard TGARCH-implied conditional value-at-risk and expected shortfall out-of-sample forecasts that rely on the notion of IID innovations. 相似文献
5.
A number of studies have found that the cross-section of stock returns reflects a risk premium for bearing downside beta; however, existing measures of downside beta have poor power for predicting returns. This paper proposes a novel measure of downside beta, the ES-implied beta, to improve the prediction of the cross-section of asset returns. The ES-implied beta explains stock returns over the same period as well as the widely used downside beta, but improves the prediction for future returns due to its high persistence. In the empirical analysis, the widely used downside beta shows a weak relation with future expected returns, but the ES-implied beta implies a statistically and economically significant risk premium of 0.6% per month and explains 0.6% of the variation in the cross-sectional returns. The effect cannot be explained by traditional cross-sectional effects and is different from the CAPM beta, the downside beta in Ang et al. (2006), coskewness, and cokurtosis. 相似文献
6.
This paper evaluates the model risk of models used for forecasting systemic and market risk. Model risk, which is the potential for different models to provide inconsistent outcomes, is shown to be increasing with market uncertainty. During calm periods, the underlying risk forecast models produce similar risk readings; hence, model risk is typically negligible. However, the disagreement between the various candidate models increases significantly during market distress, further frustrating the reliability of risk readings. Finally, particular conclusions on the underlying reasons for the high model risk and the implications for practitioners and policy makers are discussed. 相似文献
7.
This paper applies the extreme-value (EV) generalised pareto distribution to the extreme tails of the return distributions for the S&P500, FT100, DAX, Hang Seng, and Nikkei225 futures contracts. It then uses tail estimators from these contracts to estimate spectral risk measures, which are coherent risk measures that reflect a user’s risk-aversion function. It compares these to VaR and expected shortfall (ES) risk measures, and compares the precision of their estimators. It also discusses the usefulness of these risk measures in the context of clearinghouses setting initial margin requirements, and compares these to the SPAN measures typically used. 相似文献
8.
The realized-GARCH framework is extended to incorporate the two-sided Weibull distribution, for the purpose of volatility and tail risk forecasting in a financial time series. Further, the realized range, as a competitor for realized variance or daily returns, is employed as the realized measure in the realized-GARCH framework. Sub-sampling and scaling methods are applied to both the realized range and realized variance, to help deal with inherent micro-structure noise and inefficiency. A Bayesian Markov Chain Monte Carlo (MCMC) method is adapted and employed for estimation and forecasting, while various MCMC efficiency and convergence measures are employed to assess the validity of the method. In addition, the properties of the MCMC estimator are assessed and compared with maximum likelihood, via a simulation study. Compared to a range of well-known parametric GARCH and realized-GARCH models, tail risk forecasting results across seven market indices, as well as two individual assets, clearly favour the proposed realized-GARCH model incorporating the two-sided Weibull distribution; especially those employing the sub-sampled realized variance and sub-sampled realized range. 相似文献
9.
The contour maps of the error of historical and parametric estimates of the global minimum risk for large random portfolios optimized under the Expected Shortfall (ES) risk measure are constructed. Similar maps for the VaR of the ES-optimized portfolio are also presented, along with results for the distribution of portfolio weights over the random samples and for the out-of-sample and in-sample estimates for ES. The contour maps allow one to quantitatively determine the sample size (the length of the time series) required by the optimization for a given number of different assets in the portfolio, at a given confidence level and a given level of relative estimation error. The necessary sample sizes invariably turn out to be unrealistically large for any reasonable choice of the number of assets and the confidence level. These results are obtained via analytical calculations based on methods borrowed from the statistical physics of random systems, supported by numerical simulations. 相似文献
10.
We consider the problem of simulating tail loss probabilities and expected losses conditioned on exceeding a large threshold (expected shortfall) for credit portfolios. Our new idea, called the geometric shortcut, allows an efficient simulation for the case of independent obligors. It is even possible to show that, when the average default probability tends to zero, its asymptotic efficiency is higher than that of the naive algorithm. The geometric shortcut is also useful for models with dependent obligors and can be used for dependence structures modeled with arbitrary copulae. The paper contains the details for simulating the risk of the normal copula credit risk model by combining outer importance sampling with the geometric shortcut. Numerical results show that the new method is efficient in assessing tail loss probabilities and expected shortfall for credit risk portfolios. The new method outperforms all known methods, especially for credit portfolios consisting of weakly correlated obligors and for evaluating the tail loss probabilities at many thresholds in a single simulation run. 相似文献
11.
Measuring the risk of a financial portfolio involves two steps: estimating the loss distribution of the portfolio from available observations and computing a ‘risk measure’ that summarizes the risk of the portfolio. We define the notion of ‘risk measurement procedure’, which includes both of these steps, and introduce a rigorous framework for studying the robustness of risk measurement procedures and their sensitivity to changes in the data set. Our results point to a conflict between the subadditivity and robustness of risk measurement procedures and show that the same risk measure may exhibit quite different sensitivities depending on the estimation procedure used. Our results illustrate, in particular, that using recently proposed risk measures such as CVaR/expected shortfall leads to a less robust risk measurement procedure than historical Value-at-Risk. We also propose alternative risk measurement procedures that possess the robustness property. 相似文献
12.
Seungho Baek Joseph D. Cursio Seung Y. Cha 《Asia-Pacific Journal of Financial Studies》2015,44(4):497-536
This research examines the efficiency of nonparametric factor analytic approaches in measuring risk in common stocks of Korean financial firms from the risk‐management perspective. This paper shows that using only one risk factor extracted from principal component analysis, the parallel shift or market movement factor, has sufficient accuracy for downside risk measures. We assess accuracy by applying Monte Carlo simulation to obtain VaR and ES for the Korean financial sector and industries within the financial sector (banks, insurance companies, and investment andsecurity trading companies), and further estimate the risk contagious effect on financial firms. 相似文献
13.
The article contributes to the ongoing search for a market risk measure that is both coherent and elicitable. We compare two traditional measures, namely Value-at-Risk and the expected shortfall, with another relatively novel one established on the expectile probability term. Our research is based on five models: Black–Scholes, exponential tempered stable, Heston, Bates and another stochastic volatility model with a tempered stable jump correction. We apply the general Fourier inversion formula to derive closed form formulas for calculating not only the expectile based risk measure but also the Value-at-Risk and the expected shortfall. These models are calibrated by combining nonlinear programming with simulated annealing at a moving window. Additionally, we compare the generated values of the risk measures with the real ones. Last but not least, we modify the expectile based risk measure as well as the expected shortfall by introducing correction coefficients. 相似文献
14.
This paper analyzes management and control issues linked to the employment of traders who engage in proprietary trading activity
for their employer (a bank). The bank can invest in control and monitoring of these traders, and the paper evaluates the profitability
of such investments. We find that the investment in control is distorted due to interfering market microstructure effects.
The bank is inclined to underinvest in control of its traders because traders who are not too closely monitored generate extra
liquidity in the market. Bank supervision might be needed, therefore, to correct for such effects. We evaluate the effectiveness
of the value-at-risk capital adequacy requirement proposed by the Bank for International Settlements, and find that this approach
correctly targets the banks that are the most vulnerable, i.e. those that are the most at risk of underinvesting in its control
and monitoring systems.
相似文献
15.
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. 相似文献
16.
《Asia-Pacific Journal of Financial Studies》2018,47(3):449-469
This study presents an example of the linearization of a complex mean‐risk investment problem. The spectral risk measure is employed as a measure of risk and assets are assumed to have autocorrelation and conditionally heteroskedastic volatilities. Simulation results indicate that the proposed method saves a great deal of computational time. Empirical studies show that this strategy, implemented with certain trading frequency constraints, outperforms the equal‐weighted portfolio, the classical mean‐variance method, and the corresponding market index in Taiwan, the US, and Japan when considering transaction costs and different economic conditions. 相似文献
17.
18.
With the regulatory requirements for risk management, Value at Risk (VaR) has become an essential tool in determining capital reserves to protect the risk induced by adverse market movements. The fact that VaR is not coherent has motivated the industry to explore alternative risk measures such as expected shortfall. The first objective of this paper is to propose statistical methods for estimating multiple-period expected shortfall under GARCH models. In addition to the expected shortfall, we investigate a new tool called median shortfall to measure risk. The second objective of this paper is to develop backtesting methods for assessing the performance of expected shortfall and median shortfall estimators from statistical and financial perspectives. By applying our expected shortfall estimators and other existing approaches to seven international markets, we demonstrate the superiority of our methods with respect to statistical and practical evaluations. Our expected shortfall estimators likely provide an unbiased reference for setting the minimum capital required for safeguarding against expected loss. 相似文献
19.
Timotheos Angelidis Stavros Degiannakis 《Journal of International Financial Markets, Institutions & Money》2008,18(5):449-465
Volatility prediction is the key variable in forecasting the prices of options, value-at-risk and, in general, the risk that investors face. By estimating not only inter-day volatility models that capture the main characteristics of asset returns, but also intra-day models, we were able to investigate their forecasting performance for three European equity indices. A consistent relation is shown between the examined models and the specific purpose of volatility forecasts. Although researchers cannot apply one model for all forecasting purposes, evidence in favor of models that are based on inter-day datasets when their criteria based on daily frequency, such as value-at-risk and forecasts of option prices, are provided. 相似文献
20.
We use stock market data to analyze the quality of alternative models and procedures for forecasting expected shortfall (ES) at different significance levels. We compute ES forecasts from conditional models applied to the full distribution of returns as well as from models that focus on tail events using extreme value theory (EVT). We also apply the semiparametric filtered historical simulation (FHS) approach to ES forecasting to obtain 10-day ES forecasts. At the 10-day horizon we combine FHS with EVT. The performance of the different models is assessed using six different ES backtests recently proposed in the literature. Our results suggest that conditional EVT-based models produce more accurate 1-day and 10-day ES forecasts than do non-EVT based models. Under either approach, asymmetric probability distributions for return innovations tend to produce better forecasts. Incorporating EVT in parametric or semiparametric approaches also improves ES forecasting performance. These qualitative results are also valid for the recent crisis period, even though all models then underestimate the level of risk. FHS narrows the range of numerical forecasts obtained from alternative models, thereby reducing model risk. Combining EVT and FHS seems to be best approach for obtaining accurate ES forecasts. 相似文献