Applied Quantitative Finance

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. Table of Contents Cover Applied Quantitative Finance, Second Edition ISBN: 9783540691778 eISBN: 9783540691792 Preface to the 2nd Edition Preface to the 1st Edition Contents Contributors Frequently Used Notation 1 Modeling Dependencies with Copulae 1.1 Introduction 1.2 Bivariate Copulae 1.2.1 Copula Families o Simplest Copulae o Elliptical Family o Archimedean Family 1.2.2 Dependence Measures 1.3 Multivariate Copulae 1.3.1 Copula Families o Archimedean and Hierarchical Archimedean copulae 1.3.2 Dependence Measures o Generalizations 1.4 Estimation Methods Parametric margins Canonical Maximum Likelihood 1.5 Goodness-of-Fit Tests for Copulae 1.6 Simulation Methods 1.6.1 Conditional Inverse Method 1.6.2 Marshal-Olkin Method 1.7 Applications to Finance 1.7.1 Asset Allocation 1.7.2 Value-at-Risk 1.7.3 Time Series Modeling 1.8 Simulation Study and Empirical Results 1.8.1 Simulation Study o Setup of the study o Discussion of the results 1.8.2 Empirical Example 1.9 Summary Bibliography 2 Quantification of Spread Risk by Means of Historical Simulation 2.1 Introduction 2.2 Risk Categories - a Definition of Terms 2.3 Yield Spread Time Series 2.3.1 Data Analysis 2.3.2 Discussion of Results 2.4 Historical Simulation and Value at Risk 2.4.1 Risk Factor: Full Yield 2.4.2 Risk Factor: Benchmark 2.4.3 Risk Factor: Spread over Benchmark Yield 2.4.4 Conservative Approach 2.4.5 Simultaneous Simulation 2.5 Mark-to-Model Backtesting 2.6 VaR Estimation and Backtesting 2.7 P-P Plots 2.8 Q-Q Plots 2.9 Discussion of Simulation Results 2.9.1 Risk Factor: Full Yield 2.9.2 Risk Factor: Benchmark 2.9.3 Risk Factor: Spread over Benchmark Yield 2.9.4 Conservative Approach 2.9.5 Simultaneous Simulation 2.10 Internal Risk Models Bibliography 3 A Copula-Based Model of the Term Structure of CDO Tranches 3.1 Introduction 3.2 A Copula-Based Model of Basket Credit Losses Dynamics 3.3 Stochastic Processes with Dependent Increments 3.4 An Algorithm for the Propagation of Losses 3.5 Empirical Analysis 3.6 Concluding Remarks Bibliography 4 VaR in High Dimensional Systems - a Conditional Correlation Approach 4.1 Introduction 4.2 Half-Vec Multivariate GARCH Models 4.3 Correlation Models 4.3.1 Motivation 4.3.2 Log-Likelihood Decomposition 4.3.3 Constant Conditional Correlation Model 4.3.4 Dynamic Conditional Correlation Model 4.3.5 Inference in the Correlation Models 4.3.6 Generalizations of the DCC Model 4.4 Value-at-Risk 4.5 An Empirical Illustration 4.5.1 Equal and Value Weighted Portfolios 4.5.2 Estimation Results Bibliography 5 Rating Migrations 5.1 Rating Transition Probabilities 5.1.1 From Credit Events to Migration Counts 5.1.2 Estimating Rating Transition Probabilities 5.1.3 Dependent Migrations 5.1.4 Computational Aspects 5.2 Analyzing the Time-Stability of Transition Probabilities 5.2.1 Aggregation over Periods 5.2.2 Testing the Time-Stability of Transition Probabilities 5.2.3 Example 5.2.4 Computational Aspects 5.3 Multi-Period Transitions 5.3.1 Homogeneous Markov Chain 5.3.2 Bootstrapping Markov Chains 5.3.3 Rating Transitions of German Bank Borrowers 5.3.4 Portfolio Migration 5.3.5 Computational Aspects Bibliography 6 Crossand Autocorrelation in Multi-Period Credit Portfolio Models 6.1 Introduction 6.2 The Models 6.2.1 A Markov-Chain Credit Migration Model 6.2.2 The Correlated-Default-Time Model 6.2.3 A Discrete Barrier Model 6.2.4 The Time-Changed Barrier Model 6.3 Inter-Temporal Dependency and Autocorrelation 6.4 Conclusion Bibliography 7 Risk Measurement with Spectral Capital Allocation 7.1 Introduction 7.2 Review of Coherent Risk Measures and Allocation 7.2.1 Coherent Risk Measures 7.2.2 Spectral Risk Measures 7.2.3 Coherent Allocation Measures 7.2.4 Spectral Allocation Measures 7.3 Weight Function and Mixing Measure 7.4 Risk Aversion 7.5 Implementation 7.5.1 Mixing Representation 7.5.2 Density Representation 7.6 Credit Portfolio Model 7.7 Examples 7.7.1 Weighting Scheme 7.7.2 Concrete Example 7.8 Summary Bibliography 8 Valuation and VaR Computation for CDOs Using Stein s Method 8.1 Introduction 8.1.1 A Primer on CDO 8.1.2 Factor Models 8.1.3 Numerical Algorithms 8.2 First Order Gauss-Poisson Approximations 8.2.1 Stein s Method the Normal Case 8.2.2 First-Order Gaussian Approximation 8.2.3 Stein s Method the Poisson Case 8.2.4 First-Order Poisson Approximation 8.3 Numerical Tests 8.3.1 Validity Domain of the Approximations 8.3.2 Stochastic Recovery Rate Gaussian Case 8.3.3 Sensitivity Analysis 8.4 Real Life Applications 8.4.1 Gaussian Approximation 8.4.2 Poisson Approximation 8.4.3 CDO Valuation 8.4.4 Robustness of VaR Computation o Generating VaR Scenarios o Stylized Portfolio Description o Error Computation Bibliography 9 Least Squares Kernel Smoothing of the Implied Volatility Smile 9.1 Introduction 9.2 Least Squares Kernel Smoothing of the Smile 9.3 Application 9.3.1 Weighting Functions, Kernels, and Minimization Scheme 9.3.2 Data Description and Empirical Demonstration Bibliography 9.4 Proofs 10 Numerics of Implied Binomial Trees 10.1 Construction of the IBT 10.1.1 The Derman and Kani Algorithm 10.1.2 Compensation 10.1.3 Barle and Cakici Algorithm 10.2 A Simulation and a Comparison of the SPDs 10.2.1 Simulation Using the DK Algorithm 10.2.2 Simulation Using the BC Algorithm 10.2.3 Comparison with the Monte-Carlo Simulation 10.3 Example - Analysis of EUREX Data Bibliography 11 Application of Extended Kalman Filter to SPD Estimation 11.1 Linear Model 11.1.1 Linear Model for Call Option Prices 11.1.2 Estimation of State Price Density 11.1.3 State-Space Model for Call Option Prices 11.2 Extended Kalman Filter and Call Options 11.3 Empirical Results 11.3.1 Extended Kalman Filtering in Practice 11.3.2 SPD Estimation in 1995 11.3.3 SPD Estimation in 2003 11.4 Conclusions Bibliography 12 Stochastic Volatility Estimation Using Markov Chain Simulation 12.1 The Standard Stochastic Volatility Model 12.2 Extended SV Models 12.2.1 Fat Tails and Jumps o The SVt Model o The SV Model with Jump Components 12.2.2 The Relationship Between Volatility and Returns o The SV-in-Mean Model o The Asymmetric SV Model 12.2.3 The Long Memory SV Model 12.3 MCMC-Based Bayesian Inference 12.3.1 Bayes Theorem and the MCMC Algorithm 12.3.2 MCMC-Based Estimation of the Standard SV Model 12.4 Empirical Illustrations 12.4.1 The Data 12.4.2 Estimation of SV Models 12.5 Appendix 12.5.1 Derivation of the Conditional Posterior Distributions Bibliography 13 Measuring and Modeling Risk Using High-Frequency Data 13.1 Introduction 13.2 Market Microstructure E ects 13.3 Stylized Facts of Realized Volatility 13.4 Realized Volatility Models 13.5 Time-Varying Betas 13.5.1 The Conditional CAPM 13.5.2 Realized Betas 13.6 Summary Bibliography 14 Valuation of Multidimensional Bermudan Options 14.1 Introduction 14.2 Model Assumptions 14.3 Methodology 14.4 Examples 14.5 Conclusion Bibliography 15 Multivariate Volatility Models 15.1 Introduction 15.1.1 Model Specifications 15.1.2 Estimation of the BEKK-Model 15.2 An Empirical Illustration 15.2.1 Data Description 15.2.2 Estimating Bivariate GARCH 15.2.3 Estimating the (Co)Variance Processes 15.3 Forecasting Exchange Rate Densities Bibliography 16 The Accuracy of Long-term Real Estate Valuations 16.1 Introduction 16.2 Implementation 16.2.1 Computation of the Valuations 16.2.2 Data 16.3 Empirical Results 16.3.1 Characterization of the Test Market 16.3.2 Horse Race 16.4 Conclusion Bibliography 17 Locally Time Homogeneous Time Series Modelling 17.1 Introduction 17.2 Model and Setup 17.2.1 Conditional Heteroskedastic Model 17.2.2 Parametric and Local Parametric Estimation and Inference 17.2.3 Nearly Parametric Case 17.3 Methods for the Estimation of Parameters 17.3.1 Sequence of Intervals 17.3.2 Local Change Point Selection 17.3.3 Local Model Selection 17.3.4 Stagewise Aggregation 17.4 Critical Values and Other Parameters 17.5 Applications 17.5.1 Forecasting Performance for One and Multiple Steps 17.5.2 Value-at-Risk 17.5.3 A Multiple Time Series Example Bibliography 18 Simulation Based Option Pricing 18.1 Introduction 18.2 The Consumption Based Processes 18.2.1 The Snell Envelope 18.2.2 The Continuation Value, the Continuation and Exercise Regions 18.2.3 Equivalence of American Options to European Ones with Consumption Processes 18.2.4 Upper and Lower Bounds Using Consumption Processes 18.2.5 Bermudan Options 18.3 The Main Procedure 18.3.1 Local Lower Bounds 18.3.2 The Main Procedure for Constructing Upper Bounds for the Initial Position (Global Upper Bounds) 18.3.3 The Main Procedure for Constructing Lower Bounds for the Initial Position (Global Lower Bounds) 18.3.4 Kernel Interpolation 18.4 Simulations 18.4.1 Bermudan Max Calls on d Assets 18.4.2 Bermudan Basket-Put 18.5 Conclusions Bibliography 19 High-Frequency Volatility and Liquidity 19.1 Introduction 19.2 The Univariate MEM 19.3 The Vector MEM 19.4 Statistical Inference 19.5 High-Frequency Volatility and Liquidity Dynamics Bibliography 20 Statistical Process Control in Asset Management 20.1 Introduction 20.2 Review of Statistical Process Control Concepts 20.3 Applications of SPC in Asset Management 20.3.1 Monitoring Active Portfolio Managers 20.3.2 Surveillance of the Optimal Portfolio Proportions 20.4 Summary Bibliography 21 Canonical Dynamics Mechanism of Monetary Policy and Interest Rate 21.1 Introduction 21.2 Statistical Technology 21.3 Principles of the Fed Funds Rate Decision-Making 21.3.1 Fairness of In"ation Gauge 21.3.2 Neutral Interest Rate Based on Fair Gauge of In"ation 21.3.3 Monetary Policy-Making as Tight-Accommodative Cycles Along Neutral Level as Dynamic Principal 21.4 Response Curve Structure and FOMC Behavioral Analysis 21.4.1 Data Analysis and Regressive Results 21.4.2 The Structure of the FOMC s Response Curve - Model Characteristics, Interpretations 21.4.3 The Dynamics of the FFR - Model Implications 21.4.4 General Dynamic Mechanism for Long-Run Dependence of Interest Rate and In"ation 21.5 Discussions and Conclusions Bibliography Index