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This article outlines a subjective approach to estimating value at risk (VaR) and its related confidence intervals based on priors of the profit/loss distribution and its parameters. In the tradition of Bayesian statistics, this pro‐duces probability density functions for VaR that allow for subjective uncertainty. The author shows that imple‐menting this approach can be intuitive, straightforward, and applicable to any parametric VaR. One of the more difficult issues in this area is how to assess the precision of estimates: VaR estimation is usually straightforward, but estimating a confidence interval for a VaR estimate is not. This article suggests that, by inferring VaR from prior beliefs, rather than thinking of VaR as dependent on an “objective” P/L distribution, interpreting estimated confidence intervals is less problematic

This paper aims to investigate how effectively the value at risk (VaR) estimated using the student‐t distribution captures the market risk.

Two alternative VaR models, VaR‐t and VaR‐x models, are presented and compared with the benchmark model (VaR‐n model). In this study, we consider the Student‐t distribution as a fit to the empirical distribution for estimating the VaR measure, namely, VaR‐t method. Since the Student‐t distribution is criticized for its inability to capture the asymmetry of distribution of asset returns, we use the extreme value theory (EVT)‐based model, VaR‐x model, to take into account the asymmetry of distribution of asset returns. In addition, two different approaches, excess‐kurtosis and tail‐index techniques, for determining the degrees of freedom of the Student‐t distribution in VaR estimation are introduced.

The main finding of the study is that using the student‐t distribution for estimating VaR can improve the VaR estimation and offer accurate VaR estimates, particularly when tail index technique is used to determine the degrees of freedom and the confidence level exceeds 98.5 percent.

The main value is to demonstrate in detail how well the student‐t distribution behaves in estimating VaR measure for stock market index. Moreover, this study illustrates the easy process for determining the degrees of freedom of the student‐t, which is required in VaR estimation.

The purpose of this paper is to consider the problem of using the Value‐at‐Risk (VaR) technique and examine its practical implementation by Swiss Private Banks.

The paper is based on a survey originally undertaken in 2003 and updated in 2005. The research results provide details on how asset and portfolio managers understand and apply VaR methodology in their daily business.

From the banks' perspectives, VaR has both positive and negative points. It is like a common denominator for various risks. The reason is that VaR is used by portfolio managers as comparable risk measurement across different asset classes and business lines.

This analysis shows how banks can implement VaR concept more effectively through its practical implementation areas in: portfolio management decisions and asset allocation; the “what‐if” modeling of candidate traders; and measuring and monitoring market risk.

One of the most significant recent developments in the risk measurement and management area has been the emergence of value at risk (VaR). The VaR of a portfolio is the maximum loss that the portfolio will suffer over a defined time horizon, at a specified level of probability known as the VaR confidence level. The VaR has proven to be a very useful measure of market risk, and is widely used in the securities and derivatives sectors: a good example is the RiskMetrics system developed by J.P. Morgan. VaR measures based on systems such as RiskMetrics' sister, CreditMetrics, have also shown their worth as measures of credit risk, and for dealing with credit‐related derivatives. In addition, VaR can be used to measure cashflow risks and even operational risks. However, these areas are mainly concerned with risks over a relatively short time horizon, and VaR has had a more limited impact so far on the insurance and pensions literatures that are mainly concerned with longer‐term risks.

Recently, it has been suggested that macroeconomic forecasts from estimated dynamic stochastic general equilibrium (DSGE) models tend to be more accurate out-of-sample than random walk forecasts or Bayesian vector autoregression (VAR) forecasts. Del Negro and Schorfheide (2013) in particular suggest that the DSGE model forecast should become the benchmark for forecasting horse-races. We compare the real-time forecasting accuracy of the Smets and Wouters (2007) DSGE model with that of several reduced-form time series models. We first demonstrate that none of the forecasting models is efficient. Our second finding is that there is no single best forecasting method. For example, typically simple AR models are most accurate at short horizons and DSGE models are most accurate at long horizons when forecasting output growth, while for inflation forecasts the results are reversed. Moreover, the relative accuracy of all models tends to evolve over time. Third, we show that there is no support to the common practice of using large-scale Bayesian VAR models as the forecast benchmark when evaluating DSGE models. Indeed, low-dimensional unrestricted AR and VAR forecasts may forecast more accurately.

This chapter extends the univariate forecasting method proposed by Wang, Luc, and Hsiao (2013) to forecast the multivariate long memory model subject to structural breaks. The approach does not need to estimate the parameters of this multivariate system nor need to detect the structural breaks. The only procedure is to employ a VAR(k) model to approximate the multivariate long memory model subject to structural breaks. Therefore, this approach reduces the computational burden substantially and also avoids estimation of the parameters of the multivariate long memory model, which can lead to poor forecasting performance. Moreover, when there are multiple breaks, when the breaks occur close to the end of the sample or when the breaks occur at different locations for the time series in the system, our VAR approximation approach solves the issue of spurious breaks in finite samples, even though the exact orders of the multivariate long memory process are unknown. Insights from our theoretical analysis are confirmed by a set of Monte Carlo experiments, through which we demonstrate that our approach provides a substantial improvement over existing multivariate prediction methods. Finally, an empirical application to the multivariate realized volatility illustrates the usefulness of our forecasting procedure.

Small-scale VARs are widely used in macroeconomics for forecasting US output, prices, and interest rates. However, recent work suggests these models may exhibit instabilities. As such, a variety of estimation or forecasting methods might be used to improve their forecast accuracy. These include using different observation windows for estimation, intercept correction, time-varying parameters, break dating, Bayesian shrinkage, model averaging, etc. This paper compares the effectiveness of such methods in real-time forecasting. We use forecasts from univariate time series models, the Survey of Professional Forecasters, and the Federal Reserve Board's Greenbook as benchmarks.

A state space representation of a linearized DSGE model implies a VAR in terms of observable variables. The model is said be non-invertible if there exists no linear rotation of the VAR innovations which can recover the economic shocks. Non-invertibility arises when the observed variables fail to perfectly reveal the state variables of the model. The imperfect observation of the state drives a wedge between the VAR innovations and the deep shocks, potentially invalidating conclusions drawn from structural impulse response analysis in the VAR. The principal contribution of this chapter is to show that non-invertibility should not be thought of as an “either/or” proposition – even when a model has a non-invertibility, the wedge between VAR innovations and economic shocks may be small, and structural VARs may nonetheless perform reliably. As an increasingly popular example, so-called “news shocks” generate foresight about changes in future fundamentals – such as productivity, taxes, or government spending – and lead to an unassailable missing state variable problem and hence non-invertible VAR representations. Simulation evidence from a medium scale DSGE model augmented with news shocks about future productivity reveals that structural VAR methods often perform well in practice, in spite of a known non-invertibility. Impulse responses obtained from VARs closely correspond to the theoretical responses from the model, and the estimated VAR responses are successful in discriminating between alternative, nested specifications of the underlying DSGE model. Since the non-invertibility problem is, at its core, one of missing information, conditioning on more information, for example through factor augmented VARs, is shown to either ameliorate or eliminate invertibility problems altogether.