Financial Engineering with Copulas Explained [electronic resource] /
Mai, Jan-Frederik.author.
Scherer, Matthias.author.
This is a succinct guide to the application and modelling of dependence models or copulas in the financial markets. First applied to credit risk modelling, copulas are now widely used across a range of derivatives transactions, asset pricing techniques and risk models and are a core part of the financial engineer's toolkit.
Description based upon print version of record.
Cover; Half-Title; Title; Copyright; Dedication; Contents; 1 What Are Copulas?; 1.1 Two Motivating Examples; 1.1.1 Example 1: Analyzing Dependence between Asset Movements; 1.1.2 Example 2: Modeling the Dependence between Default Times; 1.2 Copulas and Sklar's Theorem; 1.2.1 The Generalized Inverse; 1.2.2 Sklar's Theorem for Survival Functions; 1.2.3 How to Apply Sklar's Theorem?; 1.3 General Copula Properties; 2 Which Rules for Handling Copulas Do I Need?; 2.1 The Fréchet-Hoeffding Bounds; 2.2 Switching from Distribution to Survival Functions
2.3 Invariance Under Strictly Monotone Transformations2.4 Computing Probabilities from a Distribution Function; 2.5 Copula Derivatives; 2.6 Constructing New Copulas from Existing Ones; 3 How to Measure Dependence?; 3.1 Pearson's Correlation Coefficient; 3.2 Concordance Measures; 3.2.1 Using Kendall's t and Spearman's ?S; 3.3 Tail Dependence; 4 What are Popular Families of Copulas?; 4.1 Gaussian Copulas; 4.1.1 Important Stylized Facts of the (Bivariate) Gaussian Copula; 4.1.2 Generalization to Elliptical Copulas; 4.2 Archimedean Copulas; 4.2.1 Stylized Facts of Archimedean Copulas
4.2.2 Hierarchical Archimedean Copulas4.3 Extreme-value Copulas; 4.3.1 Marshall-Olkin Copulas; 4.3.2 Stylized Facts of Extreme-Value Copulas; 4.4 Archimax Copulas; 5 How to SimulateMultivariate Distributions?; 5.1 How to Simulate from a Copula?; 5.1.1 Simulation Based on Analytical Techniques; 5.1.2 Simulation Along a Stochastic Model; 5.1.3 Practical Guide for the Implementation; 6 How to Estimate Parameters of a Multivariate Model?; 6.1 The Method ofMoments; 6.1.1 Some Theoretical Background; 6.2 Maximum-Likelihood Methods; 6.2.1 Perfect Information about the Marginal Laws
6.2.2 Joint Maximization Over a and ?: Full Maximum-Likelihood6.2.3 Inference Functions forMargins (IFM)Method; 6.3 Using A Rank Transformation to Obtain (Pseudo-)Samples; 6.3.1 Visualization of theMethods; 6.4 Estimation of Specific Copula Families; 6.4.1 Taylor-made Estimation Strategies for Extreme-value Copulas; 6.5 A Note on Positive Semi-Definiteness; 6.6 Some Remarks Concerning the Implementation; 7 How to Deal with Uncertainty Concerning Dependence?; 7.1 Bounds for the VaR of a Portfolio; 7.2 What is the Maximal Probability for a Joint Default?; 7.2.1 Motivation
7.2.2 Maximal Coupling8 How to Construct a Portfolio-Default Model?; 8.1 The Canonical Construction of Default Times; 8.2 Classical CopulaModels for Dependent Default Times; 8.2.1 The Portfolio-loss Distribution; 8.3 A FactorModel for CDO Pricing; 8.3.1 An Excursion to CDO Pricing; 8.3.2 Calibrating the Two Portfolio-default Models; References; Index
Includes bibliographical references and index.
This is a succinct guide to the application and modelling of dependence models or copulas in the financial markets. First applied to credit risk modelling, copulas are now widely used across a range of derivatives transactions, asset pricing techniques and risk models and are a core part of the financial engineer's toolkit.
Financial engineering.
Risk management.
Management.
Investment banking.
Securities.
Banks and banking.
Financial Engineering.
Risk Management.
Management.
Investments and Securities.
Banking.