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Measuring Risk in Complex Stochastic Systems book cover, ISBN 9780387989969

Measuring Risk in Complex Stochastic Systems

by Franke, Jurgen; Hardle, Wolfgang; Stahl, Gerhard; Bickel, P.; Diggle, P.; Fienberg, S.

ISBN13: 9780387989969
ISBN10: 038798996X
eBook ISBN(s): 9781461212140
Format: Paperback
Copyright: 2000-05-01
Publisher: Springer Verlag

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Summary

This collection of articles by leading researchers will be of interest to people working in the area of mathematical finance.

Table of Contents

Preface

v

Contributors

vii

Allocation of Economic Capital in loan portfolios

1

(18)

Ludger Overbeck

Introduction

1

(1)

Credit portfolios

2

(3)

Ability to Pay Process

3

(1)

Loss distribution

4

(1)

Economic Capital

5

(1)

Capital allocation

6

(1)

Capital allocation based on Var/Covar

6

(2)

Allocation of marginal capital

8

(1)

Contributory capital based on coherent risk measures

8

(2)

Coherent risk measures

8

(1)

Capital Definition

9

(1)

Contribution to Shortfall-Risk

10

(1)

Comparision of the capital allocation methods

10

(3)

Analytic Risk Contribution

10

(1)

Simulation procedure

10

(1)

Comparison

11

(1)

Portfolio size

12

(1)

Summary

13

(6)

Bibliography

15

(4)

Estimating Volatility for Long Holding Periods

19

(14)

Rudiger Kiesel

William Perraudin

Alex Taylor

Introduction

19

(2)

Construction and Properties of the Estimator

21

(3)

Large Sample Properties

22

(1)

Small Sample Adjustments

23

(1)

Monte Carlo Illustrations

24

(3)

Applications

27

(3)

Conclusion

30

(3)

Bibliography

30

(3)

A Simple Approach to Country Risk

33

(36)

Frank Lehrbass

Introduction

33

(1)

A Structural No-Arbitrage Approach

34

(13)

Structural versus Reduced-Form Models

34

(1)

Applying a Structural Model to Sovereign Debt

35

(1)

No-Arbitrage vs Equilibrium Term Structure

36

(1)

Assumptions of the Model

37

(2)

The Arbitrage-Free Value of a Eurobond

39

(6)

Possible Applications

45

(1)

Determination of Parameters

46

(1)

Description of Data and Parameter Setting

47

(4)

DM-Eurobonds under Consideration

47

(2)

Equity Indices and Currencies

49

(1)

Default-Free Term Structure and Correlation

50

(1)

Calibration of Default-Mechanism

50

(1)

Pricing Capability

51

(2)

Test Methodology

52

(1)

Inputs for the Closed-Form Solution

52

(1)

Model versus Market Prices

53

(1)

Hedging

53

(5)

Static part of Hedge

54

(1)

Dynamic Part of Hedge

55

(1)

Evaluation of the Hedging Strategy

56

(2)

Management of a Portfolio

58

(6)

Set Up of the Monte Carlo Approach

58

(2)

Optimality Condition

60

(2)

Application of the Optimality Condition

62

(2)

Modification of the Optimality Condition

64

(1)

Summary and Outlook

64

(5)

Bibliography

65

(4)

Predicting Bank Failures in Transition

69

(14)

Jan Hanousek

Motivation

69

(2)

Improving ``Standard'' Models of Bank Failures

71

(2)

Czech banking sector

73

(2)

Data and the Results

75

(2)

Conclusions

77

(6)

Bibliography

80

(3)

Credit Scoring using Semiparametric Methods

83

(16)

Marlene Muller

Bernd Ronz

Introduction

83

(1)

Data Description

84

(3)

Logistic Credit Scoring

87

(1)

Semiparametric Credit Scoring

88

(4)

Testing the Semiparametric Model

92

(1)

Misclassification and Performance Curves

93

(6)

Bibliography

96

(3)

On the (Ir) Relevancy of Value-at-Risk Regulation

99

(20)

Phornchanok J. Cumperayot

Jon Danielsson

Bjorn N. Jorgensen

Caspar G. de Vries

Introduction

99

(2)

VaR and other Risk Measures

101

(5)

VaR and Other Risk Measures

102

(3)

VaR as a Side Constraint

105

(1)

Economic Motives for VaR Management

106

(6)

Policy Implications

112

(2)

Conclusion

114

(5)

Bibliography

115

(4)

Backesting beyond VaR

119

(12)

Wolfgang Hardle

Gerhard Stahl

Forecast tasks and VaR Models

119

(3)

Backtesting based on the expected shortfall

122

(1)

Backtesting in Action

123

(6)

Conclusions

129

(2)

Bibliography

129

(2)

Measuring Implied Volatility Surface Risk using PCA

131

(18)

Alpha Sylla

Christophe Villa

Introduction

131

(1)

PCA of Implicit Volatility Dynamics

132

(5)

Data and Methodology

133

(1)

The results

133

(4)

Smile-consistent pricing models

137

(6)

Local Volatility Models

137

(2)

Implicit Volatility Models

139

(1)

The volatility models implementation

140

(3)

Measuring Implicit Volatility Risk using VaR

143

(6)

VaR Origins and definition

143

(2)

VaR and Principal Components Analysis

145

(2)

Bibliography

147

(2)

Detection and estimation of changes in ARCH processes

149

(12)

Piotr Kokoszka

Remigijus Leipus

Introduction

149

(3)

Testing for change-point in ARCH

152

(4)

Asymptotics under null hypothesis

153

(2)

Asymptotics under local alternatives

155

(1)

Change-point estimation

156

(5)

ARCH model

156

(2)

Extensions

158

(1)

Bibliography

159

(2)

Behaviour of Some Rank Statistics for Detecting Changes

161

(14)

Ales Slaby

Introduction

161

(1)

Limit Theorems

162

(1)

Simulations

163

(6)

Comments

169

(4)

Acknowledgements

173

(2)

Bibliography

173

(2)

A stable CAPM in the presence of heavy-tailed distributions

175

(14)

Stefan Huschens

Jeong-Ryeol Kim

Introduction

175

(1)

Empirical evidence for the stable Paretian hypothesis

176

(3)

Empirical evidence

176

(1)

Univariate und multivariate β-stable distributions

177

(2)

Stable CAPM and estimation for β-coefficients

179

(4)

Stable CAPM

180

(2)

Estimation of the β-coefficient in stable CAPM

182

(1)

Empirical analysis of bivariate symmetry test

183

(2)

Test for bivariate symmetry

183

(1)

Estimates for the β-coefficient in stable CAPM

184

(1)

Summary

185

(4)

Bibliography

185

(4)

A Tailored Suit for Risk Management: Hyperbolic Model

189

(14)

Jens Breckling

Ernst Eberlein

Philip Kokic

Introduction

189

(1)

Advantages of the Proposed Risk Management Approach

190

(1)

Mathematical Definition of the P & L Distribution

191

(2)

Estimation of the P & L using the Hyperbolic Model

193

(3)

How well does the Approach Conform with Reality

196

(1)

Extension to Credit Risk

196

(2)

Application

198

(5)

Bibliography

201

(2)

Computational Resources for Extremes

203

(12)

Torsten Kleinow

Michael Thomas

Introduction

203

(1)

Computational Resources

204

(4)

XploRe

204

(1)

Xtremes

205

(1)

Extreme Value Analysis with XploRe and Xtremes

205

(3)

Differences between XploRe and Xtremes

208

(1)

Client/Server Architectures

208

(4)

Client/Server Architecture of XploRe

209

(2)

Xtremes Corba Server

211

(1)

Conclusion

212

(3)

Bibliography

212

(3)

Confidence intervals for tail index estimator

215

(8)

Sergei Y. Novak

Confidence intervals for a tail index estimator

215

(8)

Bibliography

221

(2)

Extremes of alpha-ARCH Models

223

(22)

Christian Robert

Introduction

223

(1)

The model and its properties

224

(2)

The tails of the stationary distribution

226

(3)

Extreme value results

229

(3)

Normalizing factors

229

(1)

Computation of the extremal index

230

(2)

Empirical study

232

(7)

Distribution of extremes

235

(1)

Tail behavior

236

(2)

The extremal index

238

(1)

Proofs

239

(5)

Conclusion

244

(1)

Bibliography

245

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