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

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