Cherubini / Luciano / Vecchiato Copula Methods in Finance

Erscheinungsjahr 2004
ISBN: 978-0-470-86345-9
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 310 Seiten, E-Book

Reihe: Wiley Finance Series

Copula Methods in Finance is the first book to address the mathematics of copula functions illustrated with finance applications. It explains copulas by means of applications to major topics in derivative pricing and credit risk analysis. Examples include pricing of the main exotic derivatives (barrier, basket, rainbow options) as well as risk management issues. Particular focus is given to the pricing of asset-backed securities and basket credit derivative products and the evaluation of counterparty risk in derivative transactions.

Autoren/Hrsg.

Cherubini, Umberto

Luciano, Elisa

Vecchiato, Walter

Inhaltsverzeichnis

Preface xi
List of Common Symbols and Notations xv
1 Derivatives Pricing, Hedging and Risk Management: The Stateof the Art 1
1.1 Introduction 1
1.2 Derivative pricing basics: the binomial model 2
1.3 The Black-Scholes model 7
1.4 Interest rate derivatives 13
1.5 Smile and term structure effects of volatility 18
1.6 Incomplete markets 21
1.7 Credit risk 27
1.8 Copula methods in finance: a primer 37
2 Bivariate Copula Functions 49
2.1 Definition and properties 49
2.2 Fr´echet bounds and concordance order 52
2.3 Sklar's theorem and the probabilistic interpretationof copulas 56
2.4 Copulas as dependence functions: basic facts 70
2.5 Survival copula and joint survival function 75
2.6 Density and canonical representation 81
2.7 Bounds for the distribution functions of sum of r.v.s 84
2.8 Appendix 87
3 Market Comovements and Copula Families 95
3.1 Measures of association 95
3.2 Parametric families of bivariate copulas 112
4 Multivariate Copulas 129
4.1 Definition and basic properties 129
4.2 Frechet bounds and concordance order: the multidimensionalcase 133
4.3 Sklar's theorem and the basic probabilistic interpretation:the multidimensional case 135
4.4 Survival copula and joint survival function 140
4.5 Density and canonical representation of a multidimensionalcopula 144
4.6 Bounds for distribution functions of sums of n randomvariables 145
4.7 Multivariate dependence 146
4.8 Parametric families of n-dimensional copulas 147
5 Estimation and Calibration from Market Data 153
5.1 Statistical inference for copulas 153
5.2 Exact maximum likelihood method 154
5.3 IFM method 156
5.4 CML method 160
5.5 Non-parametric estimation 161
5.6 Calibration method by using sample dependence measures172
5.7 Application 174
5.8 Evaluation criteria for copulas 176
5.9 Conditional copula 177
6 Simulation of Market Scenarios 181
6.1 Monte Carlo application with copulas 181
6.2 Simulation methods for elliptical copulas 181
6.3 Conditional sampling 182
6.4 Marshall and Olkin's method 188
6.5 Examples of simulations 191
7 Credit Risk Applications 195
7.1 Credit derivatives 195
7.2 Overview of some credit derivatives products 196
7.3 Copula approach 202
7.4 Application: pricing and risk monitoring a CDO 210
7.5 Technical appendix 225
8 Option Pricing with Copulas 231
8.1 Introduction 231
8.2 Pricing bivariate options in complete markets 232
8.3 Pricing bivariate options in incomplete markets 239
8.4 Pricing vulnerable options 243
8.5 Pricing rainbow two-color options 253
8.6 Pricing barrier options 267
8.7 Pricing multivariate options: Monte Carlo methods 278
Bibliography 281
Index 289

Über Autor(innen)

UMBERTO CHERUBINI is Associate Professor of MathematicalFinance at the University of Bologna, and partner in PolyhedronComputational Finance, Florence, Italy. He is fellow of FERC, CassBusiness School, London and Ente Einaudi, Bank of Italy, Rome. Hehas also taught graduate finance courses at Catholic University inMilan, Hitotsubashi University in Tokyo, and is supervisor of theMarket Risk Area at the risk management education program of theItalian Banking Association (ABI). He is a member of theindependent screening committee of TLX, the new Italian structuredproducts market. Before joining the academia, he was with theEconomic Research Department of Banca Commerciale Italiana, wherehe was Head of the Risk Management Unit.
ELISA LUCIANO, Ph.D., is Full Professor of MathematicalFinance at the University of Turin (Italy), Fellow of ICER, Turin,and Associate Fellow of FERC, Cass Business School, London. Shealso teaches at the École Nationale Supérieure deCachan, Paris, and at the École Supérieure enSciences Informatiques, Université de Nice-Sophia Antipolis,France. Her main research interest is Quantitative Finance, withspecial emphasis on portfolio selection and risk measurement. Shehas published extensively in Academic journals, including theJournal of Finance and Applied Mathematical Finance.
WALTER VECCHIATO is Head of Risk Management and Researchat Veneto Banca in Montebelluna Treviso, Italy. Previously he wasHead of Credit Derivatives Analysis at Banca Intesa in Milan,Italy. He was also Professor of Applied Statistics in University ofPavia, Italy and he was Visiting Researcher in FinancialEconometrics at University of California at San Diego, La Jolla. Heenhanced his research with the presence of Nobel Economic Sciences2003 award winner Professor Robert F. Engle. He has written andpublished on quantitative finance and risk management techniques.He is a referee for many academic and practitioner journals and afrequent speaker for many symposiums on Finance worldwide.