We propose methods for evaluating density forecasts. We focus primarily on methods" that are applicable regardless of the particular user's loss function. We illustrate the methods" with a detailed simulation example, and then we present an application to density forecasting of" daily stock market returns. We discuss extensions for improving suboptimal density forecasts multi-step-ahead density forecast evaluation, multivariate density forecast evaluation for structural change and its relationship to density forecasting, and density forecast evaluation" with known loss function.

Evaluating Density Forecasts

http://directory.umm.ac.id/Data%20Elmu/jurnal/J-a/Journal%20of%20Economic%20Psychology/Vol21.Issue3.Jun2000/742.pdf

Lower partial moments as measures of perceived risk: An experimental study

We compare expected shortfall and value-at-risk (VaR) in terms of consistency with expected utility maximization and elimination of tail risk. We use the concept of stochastic dominance in studying these two aspects of risk measures. We conclude that expected shortfall is more applicable than VaR in those two aspects. Expected shortfall is consistent with expected utility maximization and is free of tail risk, under more lenient conditions than VaR.

/pdf/comparative-analyses-of-expected-shortfall-and-value-at-risk-30dlha35pb.pdf

Comparative Analyses of Expected Shortfall and Value-at-Risk (2): Expected Utility Maximization and Tail Risk

1 Allocation of Economic Capital in loan portfolios.- 1.1 Introduction.- 1.2 Credit portfolios.- 1.2.1 Ability to Pay Process.- 1.2.2 Loss distribution.- 1.3 Economic Capital.- 1.3.1 Capital allocation.- 1.4 Capital allocation based on Var/Covar.- 1.5 Allocation of marginal capital.- 1.6 Contributory capital based on coherent risk measures.- 1.6.1 Coherent risk measures.- 1.6.2 Capital Definition.- 1.6.3 Contribution to Shortfall-Risk.- 1.7 Comparision of the capital allocation methods.- 1.7.1 Analytic Risk Contribution.- 1.7.2 Simulation procedure.- 1.7.3 Comparison.- 1.7.4 Portfolio size.- 1.8 Summary.- 2 Estimating Volatility for Long Holding Periods.- 2.1 Introduction.- 2.2 Construction and Properties of the Estimator.- 2.2.1 Large Sample Properties.- 2.2.2 Small Sample Adjustments.- 2.3 Monte Carlo Illustrations.- 2.4 Applications.- 2.5 Conclusion.- 3 A Simple Approach to Country Risk.- 3.1 Introduction.- 3.2 A Structural No-Arbitrage Approach.- 3.2.1 Structural versus Reduced-Form Models.- 3.2.2 Applying a Structural Model to Sovereign Debt.- 3.2.3 No-Arbitrage vs Equilibrium Term Structure.- 3.2.4 Assumptions of the Model.- 3.2.5 The Arbitrage-Free Value of a Eurobond.- 3.2.6 Possible Applications.- 3.2.7 Determination of Parameters.- 3.3 Description of Data and Parameter Setting.- 3.3.1 DM-Eurobonds under Consideration.- 3.3.2 Equity Indices and Currencies.- 3.3.3 Default-Free Term Structure and Correlation.- 3.3.4 Calibration of Default-Mechanism.- 3.4 Pricing Capability.- 3.4.1 Test Methodology.- 3.4.2 Inputs for the Closed-Form Solution.- 3.4.3 Model versus Market Prices.- 3.5 Hedging.- 3.5.1 Static Part of Hedge.- 3.5.2 Dynamic Part of Hedge.- 3.5.3 Evaluation of the Hedging Strategy.- 3.6 Management of a Portfolio.- 3.6.1 Set Up of the Monte Carlo Approach.- 3.6.2 Optimality Condition.- 3.6.3 Application of the Optimality Condition.- 3.6.4 Modification of the Optimality Condition.- 3.7 Summary and Outlook.- 4 Predicting Bank Failures in Transition.- 4.1 Motivation.- 4.2 Improving "Standard" Models of Bank Failures.- 4.3 Czech banking sector.- 4.4 Data and the Results.- 4.5 Conclusions.- 5 Credit Scoring using Semiparametric Methods.- 5.1 Introduction.- 5.2 Data Description.- 5.3 Logistic Credit Scoring.- 5.4 Semiparametric Credit Scoring.- 5.5 Testing the Semiparametric Model.- 5.6 Misclassification and Performance Curves.- 6 On the (Ir) Relevancy of Value-at-Risk Regulation.- 6.1 Introduction.- 6.2 VaR and other Risk Measures.- 6.2.1 VaR and Other Risk Measures.- 6.2.2 VaR as a Side Constraint.- 6.3 Economic Motives for VaR Management.- 6.4 Policy Implications.- 6.5 Conclusion.- 7 Backtesting beyond VaR.- 7.1 Forecast tasks and VaR Models.- 7.2 Backtesting based on the expected shortfall.- 7.3 Backtesting in Action.- 7.4 Conclusions.- 8 Measuring Implied Volatility Surface Risk using PCA.- 8.1 Introduction.- 8.2 PCA of Implicit Volatility Dynamics.- 8.2.1 Data and Methodology.- 8.2.2 The results.- 8.3 Smile-consistent pricing models.- 8.3.1 Local Volatility Models.- 8.3.2 Implicit Volatility Models.- 8.3.3 The volatility models implementation.- 8.4 Measuring Implicit Volatility Risk using VaR.- 8.4.1 VaR: Origins and definition.- 8.4.2 VaR and Principal Components Analysis.- 9 Detection and estimation of changes in ARCH processes.- 9.1 Introduction.- 9.2 Testing for change-point in ARCH.- 9.2.1 Asymptotics under null hypothesis.- 9.2.2 Asymptotics under local alternatives.- 9.3 Change-point estimation.- 9.3.1 ARCH model.- 9.3.2 Extensions.- 10 Behaviour of Some Rank Statistics for Detecting Changes.- 10.1 Introduction.- 10.2 Limit Theorems.- 10.3 Simulations.- 10.4 Comments.- 10.5 Acknowledgements.- 11 A stable CAPM in the presence of heavy-tailed distributions.- 11.1 Introduction.- 11.2 Empirical evidence for the stable Paretian hypothesis.- 11.2.1 Empirical evidence.- 11.2.2 Univariate und multivariate ?-stable distributions.- 11.3 Stable CAPM and estimation for ?-coefficients.- 11.3.1 Stable CAPM.- 11.3.2 Estimation of the ?-coefficient in stable CAPM.- 11.4 Empirical analysis of bivariate symmetry test.- 11.4.1 Test for bivariate symmetry.- 11.4.2 Estimates for the ?-coefficient in stable CAPM.- 11.5 Summary.- 12 A Tailored Suit for Risk Management: Hyperbolic Model.- 12.1 Introduction.- 12.2 Advantages of the Proposed Risk Management Approach.- 12.3 Mathematical Definition of the P & L Distribution.- 12.4 Estimation of the P & L using the Hyperbolic Model.- 12.5 How well does the Approach Conform with Reality.- 12.6 Extension to Credit Risk.- 12.7 Application.- 13 Computational Resources for Extremes.- 13.1 Introduction.- 13.2 Computational Resources.- 13.2.1 XploRe.- 13.2.2 Xtremes.- 13.2.3 Extreme Value Analysis with XploRe and Xtremes.- 13.2.4 Differences between XploRe and Xtremes.- 13.3 Client/Server Architectures.- 13.3.1 Client/Server Architecture of XploRe.- 13.3.2 Xtremes CORBA Server.- 13.4 Conclusion.- 14 Confidence intervals for a tail index estimator.- 14.1 Confidence intervals for a tail index estimator.- 15 Extremes of alpha-ARCH Models.- 15.1 Introduction.- 15.2 The model and its properties.- 15.3 The tails of the stationary distribution.- 15.4 Extreme value results.- 15.4.1 Normalizing factors.- 15.4.2 Computation of the extremal index.- 15.5 Empirical study.- 15.5.1 Distribution of extremes.- 15.5.2 Tail behavior.- 15.5.3 The extremal index.- 15.6 Proofs.- 15.7 Conclusion.

Measuring Risk in Complex Stochastic Systems

The FASB recently issued Proposed Statement of Financial Accounting Standards, Accounting for Hedging Activities: An Amendment of FASB Statement No 133 The proposed standard simplifies the accounting for hedging activities and generally increases the appeal of hedge accounting In this report we survey firms' reporting practices and examine hedges and hedge accounting generally and seek to determine why firms may decide not to designate derivatives as hedges for accounting purposes In reviewing the reports of a large sample of firms, we find the following four explicit reasons why companies may decide not to designate derivatives as accounting hedges: (1) the substantial cost of documentation and ongoing monitoring of designated hedges; (2) the availability of natural hedges that can be highly effective; (3) a new accounting standard that broadens the applicability of natural or economic hedges; and (4) qualifying hedges are not available or are too costly or documentation is untimely, inadequate, or unavailable In addition, a fifth reason, not offered as such by the surveyed firms, is the increased risk of restatement that accompanies hedge accounting The proposed standard combined with the recently-released SFAS 159, The Fair Value Option for Financial Assets and Liabilities, offer companies a welcome relief to the onerous accounting and reporting requirements of SFAS 133

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1346112_code438461.pdf?abstractid=1346112&mirid=5

The non-designation of derivatives as hedges for accounting purposes

We demonstrate that limiting the value at risk may increase banks' risk taking while the expected return remains unchanged. Therefore, value at risk is neither a good internal nor a good regulatory risk measure. The lower partial moment one is shown to be a superior alternative.

Effects on Risk Taking Resulting from Limiting the Value at Risk or the Lower Partial Moment One

Der Einfluß einer Begrenzung des Value at Risk oder des Lower Partial Moment One auf die Risikoübernahme

Value at risk is en vogue as an internal measure of risk which is also accepted by regulators. The paper provides a critical appraisal based on comparisons with the related concepts of stochastic dominance and lower partial moments. In particular, we find that value at risk contradicts second-degree stochastic dominance and thus expected utility maximization for non-satiated, risk averse individuals. This might lead to regulation having adverse effects on banks’ risk taking.

On the Compatibility of Value at Risk, Other Risk Concepts, and Expected Utility Maximization

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Effects on Risk Taking Resulting from Limiting the Value at Risk or the Lower Partial Moment One

Der Einfluß einer Begrenzung des Value at Risk oder des Lower Partial Moment One auf die Risikoübernahme

On the Compatibility of Value at Risk, Other Risk Concepts, and Expected Utility Maximization