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Measuring Risk in Complex Stochastic Systems
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Table of Contents

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.

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