Applied Quantitative Finance

Description

Recent years have witnessed a growing importance of quantitative methods in both financial research and industry. This development requires the use of advanced techniques on a theoretical and applied level, especially when it comes to the quantification of risk and the valuation of modern financial products. Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance. Themes that are dominant in current research and which are presented in this book include among others the valuation of Collaterized Debt Obligations (CDOs), the high-frequency analysis of market liquidity, the pricing of Bermuda options and realized volatility. All Quantlets for the calculation of the given examples are downloadable from the Springer web pages. Preface to the Third Edition Contents Part I Market Risk 1 VaR in High Dimensional Systems-A Conditional Correlation Approach 1.1 Introduction 1.2 Half-Vec Multivariate GARCH Models 1.3 Correlation Models 1.3.1 Motivation 1.3.2 Log-Likelihood Decomposition 1.3.3 Constant Conditional Correlation Model 1.3.4 Dynamic Conditional Correlation Model 1.3.5 Inference in the Correlation Models 1.3.6 Generalizations of the DCC Model 1.4 Value-at-Risk 1.5 An Empirical Illustration 1.5.1 Equal and Value Weighted Portfolios 1.5.2 Estimation Results References 2 Multivariate Volatility Models 2.1 Introduction 2.1.1 Model Specifications 2.1.2 Estimation of the BEKK Model 2.2 An Empirical Illustration 2.2.1 Data Description 2.2.2 Estimating Bivariate GARCH 2.2.3 Estimating the (co)variance Processes 2.3 Forecasting Exchange Rate Densities References 3 Portfolio Selection with Spectral Risk Measures 3.1 Introduction 3.2 Backgrounds 3.2.1 Coherent Measures of Risk 3.2.2 Utility Function 3.2.3 Spectral Measures of Risk 3.2.4 Vine Copulae: C- and D-Vines 3.3 Methodology 3.4 Simulation Study 3.4.1 A 2-Dimensional Case 3.4.2 The Impacts of Tail-Dependence 3.4.3 The Impact of the Degrees of Risk Aversion 3.5 Empirical Studies 3.6 Concluding Remarks References 4 Implementation of Local Stochastic Volatility Model in FX Derivatives 4.1 Introduction 4.2 Model Calibration 4.3 Pricing (Backward PDE and Forward Monte Carlo) 4.4 Empirical Results 4.5 Conclusion and Future Works References Part II Credit Risk 5 Estimating Distance-to-Default with a Sector-Specific Liability Adjustment via Sequential Monte Carlo 5.1 Introduction 5.2 DTD Subject to a Sector-Specific Liability Adjustment 5.2.1 The Structural Credit Risk Model with a Common Liability Adjustment 5.2.2 The Transformed-Data Likelihood 5.3 Parameter Estimation by the Density-Tempered Expanding-Data Sequential Monte Carlo 5.4 Empirical Implementation 5.4.1 Data 5.4.2 Results References 6 Risk Measurement with Spectral Capital Allocation 6.1 Introduction 6.2 Review of Coherent Risk Measures and Allocation 6.2.1 Coherent Risk Measures 6.2.2 Spectral Risk Measures 6.2.3 Coherent Allocation Measures 6.2.4 Spectral Allocation Measures 6.3 Weight Function and Mixing Measure 6.4 Risk Aversion 6.5 Implementation 6.5.1 Mixing Representation 6.5.2 Density Representation 6.6 Credit Portfolio Model 6.7 Examples 6.7.1 Weighting Scheme 6.7.2 Concrete Example 6.8 Summary References 7 Market Based Credit Rating and Its Applications 7.1 Introduction 7.2 Methodology 7.2.1 Modeling and Forecasting 7.2.2 Clustering 7.3 Empirical Analysis 7.3.1 Modeling and Forecasting 7.3.2 Cluster Analysis 7.3.3 Discussion 7.4 Concluding Remarks References 8 Using Public Information to Predict Corporate Default Risk 8.1 Introduction 8.2 Literature Review 8.3 Econometric Models 8.3.1 Logistic Models for Default Rate 8.3.2 Default Models Including News Information 8.3.3 Bayesian Network Model 8.4 Extracting News Information 8.4.1 News Keywords 8.4.2 Keyword Conversion 8.5 Empirical Analysis and Results 8.5.1 Empirical Models 8.5.2 Variable Selection 8.5.3 Adding News Variables 8.6 Conclusions References 9 Stress Testing in Credit Portfolio Models 9.1 Introduction 9.2 Quantitative Framework for Stress Testing 9.2.1 Definition of Asset and Default Correlations 9.3 Factor Stress Methodology 9.3.1 Specification of Stress Scenarios 9.3.2 Implementation of Stress Scenarios in Credit Portfolio Models 9.3.3 Calculation of Stressed Risk Capital 9.3.4 Case Study 9.4 Stressed Correlations and Default Probabilities 9.4.1 Distribution of Model Variables 9.4.2 Asset Correlations Under Stress 9.4.3 Default Probabilities and Default Correlations Under Stress 9.5 Risk Measures 9.6 Conclusion References 10 Penalized Independent Factor 10.1 Introduction 10.2 Data 10.3 Penalized Independent Factor 10.3.1 Independent Component's Density: NIG 10.3.2 Penalty Function: SCAD 10.3.3 Estimation 10.3.4 Property of Estimator 10.4 Simulation 10.4.1 Experiment 1: 3 Dimensional Data 10.4.2 Experiment 2: Large Dimensional Data 10.5 Real Data Analysis 10.6 Conclusion References 11 Term Structure of Loss Cascades in Portfolio Securitisation 11.1 Introduction 11.2 Loss Distribution of Uniform Portfolio 11.3 Time Slicing 11.4 Loss Cascades 11.5 Results 11.5.1 Other Loss Distributions 11.5.2 Variable Portfolio Quality 11.6 Conclusion References 12 Credit Rating Score Analysis 12.1 Introduction 12.2 Principal Components Analysis of Factor Scores 12.2.1 Cross Validation via Leave-One-Out 12.3 Adjusted Weighting of Factor Scores 12.3.1 Match Expert Score 12.3.2 Cross Validation via Leave-One-Out 12.3.3 Widest Projection Spread 12.4 Conclusion Reference Part III Dynamics Risk Measurement 13 Copulae in High Dimensions: An Introduction 13.1 Introduction 13.2 Bivariate Copula 13.2.1 Copula Families 13.2.2 Bivariate Copula and Dependence Measures 13.3 Multivariate Copula: Primer and State-of-Art 13.3.1 Extensions of Simple and Elliptical Bivariate Copulae 13.3.2 Hierarchical Archimedean Copula 13.3.3 Factor Copula 13.3.4 Vine Copula 13.4 Estimation Methods 13.4.1 Parametric Margins 13.4.2 Non-parametric Margins 13.5 Goodness-of-Fit Tests for Copulae 13.6 Empirical Study 13.7 Conclusion References 14 Measuring and Modeling Risk Using High-Frequency Data 14.1 Introduction 14.2 Market Microstructure Effects 14.3 Stylized Facts of Realized Volatility 14.4 Realized Volatility Models 14.5 Time-Varying Betas 14.5.1 The Conditional CAPM 14.5.2 Realized Betas 14.6 Summary References 15 Measuring Financial Risk in Energy Markets 15.1 Introduction 15.2 Methodology and Data 15.3 Backtesting Results 15.4 Conclusion References 16 Risk Analysis of Cryptocurrency as an Alternative Asset Class 16.1 Introduction 16.2 Data Collection 16.2.1 Parse the Balance Information of Each Address from the Downloaded Block Chain Using C++ 16.2.2 Parse Other Fundamental Variables of Bitcoin 16.2.3 Historical Price Data for Auroracoin Are from a Data Provider Named Myip 16.2.4 Parse Other Fundamental Variables of Auroracoin from Online Block Chain Explorer Using Python 16.3 Methodology 16.4 Empirical Results 16.4.1 Data Visualization 16.4.2 Power-Law Estimation and Empirical Analysis 16.5 Other Risk Analysis 16.6 Conclusion References 17 Time Varying Quantile Lasso 17.1 Introduction 17.2 Lasso Method 17.2.1 Lasso as an Optimization Problem 17.2.2 Choosing the Penalization Parameter 17.2.3 Algorithms to Solve Lasso 17.3 Simulation Study 17.3.1 Penalty λ Dependent on Variance σ2 17.3.2 Penalty λ Dependent on Model Size q 17.3.3 Penalty λ Dependent on Design 17.3.4 All Factors Affecting the Value of λ 17.4 Empirical Analysis 17.4.1 Data Description 17.4.2 Construction of Time Series of λ"0362λ 17.4.3 λ"0362λ and Systemic Risk Measures References 18 Dynamic Topic Modelling for Cryptocurrency Community Forums 18.1 Introduction 18.2 Data 18.3 Topic Modelling 18.4 Preprocessing 18.5 Trends 18.6 Choosing K and Analysis 18.7 Detection 18.8 Conclusion References 19 Erratum to: Copulae in High Dimensions: An Introduction Erratum to:Chapter 13 in: W.K. Härdle et al. (eds.), Applied Quantitative Finance, Statistics and Computing, https://doi.org/10.1007/978-3-662-54486-0_13