Risk Measures for the 21st Century

The last five years have witnessed a great momentum in the research into measures of financial risk. After many years of ad–hoc and non–consistent measures, now the problem is finally well formulated and some useful and very user–friendly solutions have been proposed. These new measures of risk should be of great interest for investors, financial institutions as well as for regulators. 
Under the editorship of Professor Giorgio Szego of the University of Rome "La Sapienza", this book is a collection of the revised and updated papers from prestigious international specialists who are leaders in their field, amongst whom is Robert Engle, a newly–announced Nobel prize–winner in finance. These authors bring a broad perspective across a wide selection of topics, ranging from the critique of some currently used methods, like Value at Risk, to the presentation of some correct risk measures and of some advanced application
The book provides a detailed and up–to–date reference for researchers within academia, and risk managers or financial engineers.


Spis treści:
About the Contributors.
1 On the (Non)Acceptance of Innovations (Giorgio Szegö).
1.1 Introduction.
1.2 The path towards acceptance of previous innovations.
1.3 How to answer.
1.4 Conclusions.
References.
PART I: RISK MEASURES AND REGULATION.
2 The Emperor has no Clothes: Limits to Risk Modelling (Jón Daníelsson).
2.1 Introduction.
2.2 Risk modelling and endogenous response.
2.3 Empirical properties of risk models.
2.3.1 Background.
2.3.2 Robustness of risk forecasts.
2.3.3 Risk volatility.
2.3.4 Model estimation horizon.
2.3.5 Holding periods and loss horizons.
2.3.6 Non–linear dependence.
2.4 The concept of (regulatory) risk.
2.4.1 Volatility.
2.4.2 Value–at–risk.
2.4.3 Coherent risk measures.
2.4.4 Moral hazard – ; massaging VaR numbers.
2.4.5 The regulatory 99% risk level.
2.5 Implications for regulatory design.
2.6 Conclusion.
Acknowledgements.
Appendix A: Empirical study.
References.
3 Upgrading Value–at–Risk from Diagnostic Metric to Decision Variable: A Wise Thing to Do? (Henk Grootveld and Winfried G. Hallerbach).
3.1 Introduction.
3.2 Preliminaries.
3.2.1 VaR and downside risk.
3.2.2 Downside risk portfolio selection.
3.2.3 Incomplete risk meaure.
3.2.4 Computational issues.
3.3 The mean–value–at–risk portfolio selection model.
3.3.1 Deriving the mean–VaR portfolio selection model.
3.3.2 Distinctive properties of the mean–VaR portfolio selection model.
3.3.3 Solving the mean–VaR portfolio selection problem.
3.4 The mean–value–at–risk portfolio selection model in practice.
3.4.1 Data.
3.4.2 Methodology.
3.4.3 Results.
3.5 Conclusions.
Acknowledgements.
References.
4 Concave Risk Measures in International Capital Regulation (Imre Kondor, András Szepessy and Tünde Ujvárosi).
4.1 Introduction.
4.2 Risk measures implied by the trading book regulation.
4.2.1 Specific risk of bonds.
4.2.2 Foreign exchange.
4.2.3 Equity risk.
4.2.4 The general risk of bonds.
4.3 Conclusion.
Acknowledgements.
References.
5 Value–at–Risk, Expected Shortfall and Marginal Risk Contribution (Hans Rau–Bredow).
5.1 Introduction.
5.2 Value–at–risk as a problematic risk measure.
5.3 Derivatives of value–at–risk and expected shortfall.
5.3.1 Preliminary remarks.
5.3.2 First and second derivative of value–at–risk.
5.3.3 First and second derivative of expected shortfall.
5.4 Outlook.
Appendix.
References.
6 Risk Measures for Asset Allocation Models (Rosella Giacometti and Sergio Ortobelli Lozza).
6.1 Introdu ction.
6.2 Portfolio risk measures.
6.2.1 Safety risk measures.
6.2.2 Dispersion measures.
6.3 Portfolio choice comparison based on historical data.
6.4 Portfolio choice comparison based on simulated returns.
6.4.1 Portfolio choice comparison with jointly Gaussian returns.
6.4.2 Portfolio choice comparison with jointly stable non–Gaussian returns.
6.5 Conclusions.
Acknowledgements.
References.
7 Regulation and Incentives for Risk Management in Incomplete Markets (J´on Daníelsson, Bjørn N. Jorgensen and Casper G. de Vries).
7.1 Introduction.
7.1.1 Complete and incomplete markets.
7.2 Moral hazard regarding project choice.
7.2.1 Deposit insurance and moral hazard.
7.2.2 Threat of an alternative project choice.
7.3 Moral hazard regarding risk management.
7.3.1 The basic principal–agent model.
7.3.2 Supervision.
7.4 Risk monitoring and risk management.
7.4.1 Coarser risk monitoring without regulation.
7.4.2 Indirect risk monitoring with regulation.
7.4.3 Finer risk monitoring: no regulation.
7.4.4 Direct risk monitoring with regulation.
7.4.5 Evaluation.
7.5 Conclusion.
References.
8 Granularity Adjustment in Portfolio Credit Risk Measurement (Michael B. Gordy).
8.1 Introduction.
8.2 Granularity adjustment of VaR for homogeneous portfolios.
8.3 Granularity adjustment of ES for homogeneous portfolios.
8.4 Application to heterogeneous portfolios.
Appendix: Wilde’s formula for ?.
Acknowledgements.
References.
9 A Comparison of Value–at–Risk Models in Finance (Simone Manganelli and Robert F. Engle).
9.1 Introduction.
9.2 Value–at–risk methodologies.
9.2.1 Parametric models.
9.2.2 Nonparametric models.
9.2.3 Semiparametric models.
9.3 Expected shortfall.
9.4 Monte Carlo simulation.
9.4.1 Simulation study of the threshold choice for EVT.
9.4.2 Comparison of quantile methods performance.
9.5 Conclusion.
References.
Appendix: Tables.
PART II: NEW RISK MEASURES.
10 Coherent Representations of Subjective Risk–Aversion (Carlo Acerbi).
10.1 Forewords and motivations.
10.1.1 In defense of axiomatics.
10.1.2 Scope and objectives.
10.1.3 Outline of the work.
10.2 Building a risk measure: the expected shortfall.
10.2.1 A close look into VaR’s definition.
10.2.2 A natural remedy to probe the tail: the expected shortfall.
10.2.3 Coherency of ES.
10.2.4 Estimation of ES.
10.3 Spectral measures of risk.
10.3.1 Estimation of spectral measures of risk.
10.3.2 Characterization of spectral measures via additional conditions.
10.3.3 Spectral measures and capital adequacy.
10.4 Optimization of spectral measures of risk.
10.4.1 Coherent measures and convex risk surfaces.
10.4.2 Minimization of expected shortfall.
10.4.3 Minimization of general spectral measures.
10.4.4 Risk–reward optimization.
10.5 Statistical errors of spectral measures of risk.
10.5.1 Variance of the estimator.
10.5.2 Some meaningful examples.
Acknowledgements.
References.
11 Spectral Risk Measures for Credit Portfolios (Claudio Albanese and Stephan Lawi).
11.1 Introduction.
11.2 Test–portfolios with market risk and entity–specific risk.
11.3 Properties of risk measures.
11.4 Discussion of test–portfolios.
11.5 Concluding remarks.
Acknowledgements.
References.
Appendix: Tables.
12 Dynamic Convex Risk Measures (Marco Frittelli and Emanuela Rosazza Gianin).
12.1 Introduction.
12.1.1 Notation.
12.1.2 Axioms.
12.1.3 Coherent risk measures.
12.2 Convex risk measures.
12.2.1 Representation of convex risk measures.
12.2.2 Law–invariant convex risk measures.
12.3 Indifferent prices and risk measures.
12.4 Dynamic risk measures.
12.5 Appendix.
References.
13 A Risk Measure