Copula Methods in Finance [Hardcover]

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.

Preface xi

List of Common Symbols and Notations xv

1 Derivatives Pricing, Hedging and Risk Management: The State of 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 interpretation of 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 famls!