Copula methods in finance

TLDR: The author examines the implications of Sklar's theorem in financial applications: toward a non-Black-Scholes world for derivatives pricing, Hedging and Risk Management and the application of VaR bounds to copulas.

Abstract: PrefaceList of Common Symbols and Notations1 Derivatives Pricing, Hedging and Risk Management: The State of the Art11 Introduction12 Derivative pricing basics: the binomial model121 Replicating portfolios122 No-arbitrage and the risk-neutral probability measure123 No-arbitrage and the objective probability measure124 Discounting under different probability measures125 Multiple states of the world13 The Black-Scholes model131 Ito's lemma132 Girsanov theorem133 The martingale property134 Digital options14 Interest rate derivatives141 Affine factor models142 Forward martingale measure143 LIBOR market model15 Smile and term structure effects of volatility151 Stochastic volatility models152 Local volatility models153 Implied probability16 Incomplete markets161 Back to utility theory162 Super-hedging strategies17 Credit risk171 Structural models172 Reduced form models173 Implied default probabilities174 Counterparty risk18 Copula methods in finance: a primer181 Joint probabilities, marginal probabilities and copula functions182 Copula functions duality183 Examples of copula functions184 Copula functions and market comovements185 Tail dependence186 Equity-linked products187 Credit-linked products2 Bivariate Copula Functions21 Definition and properties22 Frechet bounds and concordance order23 Sklar's theorem and the probabilistic interpretation of copulas231 Sklar's theorem232 The subcopula in Sklar's theorem233 Modeling consequences234 Sklar's theorem in financial applications: toward a non-Black-Scholes world24 Copulas as dependence functions: basic facts241 Independence242 Comonotonicity243 Monotone transforms and copula invariance244 An application: VaR trade-off25 Survival copula and joint survival function251 An application: default probability with exogenous shocks26 Density and canonical representation27 Bounds for the distribution functions of sum of rvs271 An application: VaR bounds28 Appendix3 Market Comovements and Copula Families31 Measures of association311 Concordance312 Kendall's tau313 Spearman's rhoS314 Linear correlation315 Tail dependence316 Positive quadrant dependency32 Parametric families of bivariate copula321 The bivariate Gaussian copula322 The bivariate Student's t copula323 The Fr-echet family324 Archimedean copulas325 The Marshall-Olkin copula4 Multivariate Copulas41 Definition and basic properties42 Frechet bounds and concordance order: the multidimensional case43 Sklar's theorem and the basic probabilistic interpretation: the multidimensional case431 Modeling consequences44 Survival copula and joint survival function45 Density and canonical representation of a multidimensional copula46 Bounds for distribution functions of sums of n random variables47 Multivariate dependence48 Parametric families of n-dimensional copulas481 The multivariate Gaussian copula482 The multivariate Student's t copula483 The multivariate dispersion copula484 Archimedean copulas5 Estimation and Calibration from Market Data51 Statistical inference for copulas52 Exact maximum likelihood method521 Examples53 IFM method531 Application: estimation of the parametric copula for market data54 CML method541 Application: estimation of the correlation matrix for a Gaussian copula55 Non-parametric estimation551 The empirical copula552 Kernel copula56 Calibration method by using sample dependence measures57 Application58 Evaluation criteria for copulas59 Conditional copula591 Application to an equity portfolio6 Simulation of Market Scenarios61 Monte Carlo application with copulas62 Simulation methods for elliptical copulas63 Conditional sampling631 Clayton n-copula632 Gumbel n-copula633 Frank n-copula64 Marshall and Olkin's method65 Examples of simulations7 Credit Risk Applications71 Credit derivatives72 Overview of some credit derivatives products721 Credit default swap722 Basket default swap723 Other credit derivatives products724 Collateralized debt obligation (CDO)73 Copula approach731 Review of single survival time modeling and calibration732 Multiple survival times: modeling733 Multiple defaults: calibration734 Loss distribution and the pricing of CDOs735 Loss distribution and the pricing of homogeneous basket default swaps74 Application: pricing and risk monitoring a CDO741 Dow Jones EuroStoxx50 CDO742 Application: basket default swap743 Empirical application for the EuroStoxx50 CDO744 EuroStoxx50 pricing and risk monitoring745 Pricing and risk monitoring of the basket default swaps75 Technical appendix751 Derivation of a multivariate Clayton copula density752 Derivation of a 4-variate Frank copula density753 Correlated default times754 Variance-covariance robust estimation755 Interest rates and foreign exchange rates in the analysis8 Option Pricing with Copulas81 Introduction82 Pricing bivariate options in complete markets821 Copula pricing kernels822 Alternative pricing techniques83 Pricing bivariate options in incomplete markets831 Frcicing: super-replication in two dimensions832 Copula pricing kernel84 Pricing vulnerable options841 Vulnerable digital options842 Pricing vulnerable call options843 Pricing vulnerable put options844 Pricing vulnerable options in practice85 Pricing rainbow two-color options851 Call option on the minimum of two assets852 Call option on the maximum of two assets853 Put option on the maximum of two assets854 Put option on the minimum of two assets855 Option to exchange856 Pricing and hedging rainbows with smiles: Everest notes86 Pricing barrier options861 Pricing call barrier options with copulas: the general framework862 Pricing put barrier option: the general framework863 Specifying the trigger event864 Calibrating the dependence structure865 The reflection copula87 Pricing multivariate options: Monte Carlo methods871 Application: basket optionBibliographyIndex