Applied Quantitative Finance

Transcription

1 W. Härdle T. Kleinow G. Stahl Applied Quantitative Finance Theory and Computational Tools m Springer

2 Preface xv Contributors xix Frequently Used Notation xxi I Value at Risk 1 1 Approximating Value at Risk in Conditional Gaussian Models 3 Stefan R. Jaschke and Yuze Jiang 1.1 Introduction The Practical Need Statistical Modeling for VaR VaR Approximations Pros and Cons of Delta-Gamma Approximations General Properties of Delta-Gamma-Normal Models Cornish-Fisher Approximations Derivation Properties Fourier Inversion 16 "ff;"

3 IV Error Analysis Tail Behavior Inversion of the cdf minus the Gaussian Approximation Variance Reduction Techniques in Monte-Carlo Simulation Monte-Carlo Sampling Method Partial Monte-Carlo with Importance Sampling XploRe Examples 30 2 Applications of Copulas for the Caiculation of Value-at-Risk 35 Jörn Rank and Thomas Siegl 2.1 Copulas Definition Sklar's Theorem Examples of Copulas Further Important Properties of Copulas Computing Value-at-Risk with Copulas Selecting the Marginal Distributions Selecting a Copula Estimating the Copula Parameters Generating Scenarios - Monte Carlo Value-at-Risk Examples Results 47 3 Quantification of Spread Risk by Means of Historical Simulation 51 Christoph Frisch and Germar Knöchlein 3.1 Introduction Risk Categories - a Definition of Terms 51

4 Nc- v 3.3 Descriptive Statistics of Yield Spread Time Series Data Analysis with XploRe Discussion of Results Historical Simulation and Value at Risk Risk Factor: Füll Yield Risk Factor: Benchmark Risk Factor: Spread over Benchmark Yield Conservative Approach Simultaneous Simulation Mark-to-Model Backtesting VaR Estimation and Backtesting with XploRe P-P Plots Q-Q Plots Discussion of Simulation Results Risk Factor: Füll Yield Risk Factor: Benchmark Risk Factor: Spread over Benchmark Yield Conservative Approach Simultaneous Simulation XploRe for Internal Risk Models 81 II Credit Risk 85 4 Rating Migrations 87 Steffi Hose, Stefan Huschens and Robert Wania 4.1 Rating Transition Probabilities From Credit Events to Migration Counts 88

5 vi Estimating Rating Transition Probabilities Dependent Migrations Computation and Quantlets Analyzing the Time-Stability of Transition Probabilities Aggregation over Periods Are the Transition Probabilities Stationary? Computation and Quantlets Examples with Graphical Presentation Multi-Period Transitions Time Homogeneous Markov Chain Bootstrapping Markov Chains Computation and Quantlets Rating Transitions of German Bank Borrowers Portfolio Migration Sensitivity analysis of credit portfolio modeis 111 Rüdiger Kiesel and Torsten Kleinow 5.1 Introduction Construction of portfolio credit risk modeis Dependence modelling Factor modelling Copula modelling Simulations Random sample generation Portfolio results 120

6 vii lll Implied Volatility The Analysis of Implied Volatilities 127 Matthias R. Fengler, Wolfgang Härdle and Peter Schmidt 6.1 Introduction The Implied Volatility Surface Calculating the Implied Volatility Surface smoothing Dynamic Analysis Data description PCA of ATM Implied Volatilities Common PCA of the Implied Volatility Surface How Precise Are Price Distributions Predicted by IBT? 145 Wolfgang Härdle and Jim Zheng 7.1 Implied Binomial Trees The Derman and Kani (D & K) algorithm Compensation Barle and Cakici (B & C) algorithm A Simulation and a Comparison of the SPDs Simulation using Derman and Kani algorithm Simulation using Barle and Cakici algorithm Comparison with Monte-Carlo Simulation Example - Analysis of DAX data Estimating State-Price Densities with Nonparametric Regression 171 Kim Huynh, Pierre Kervella and Jun Zheng 8.1 Introduction 171 r

7 viii 8.2 Extracting the SPD using Call-Options Black-Scholes SPD Semiparametric estimation of the SPD Estimating the call pricing function Further dimension reduction Local Polynomial Estimation An Example: Application to DAX data Data SPD, delta and gamma Bootstrap confidence bands Comparison to Implied Binomial Trees Trading on Deviations of Implied and Historical Densities 197 Oliver Jim Blaskowitz and Peter Schmidt 9.1 Introduction Estimation of the Option Implied SPD Application to DAX Data Estimation of the Historical SPD The Estimation Method Application to DAX Data Comparison of Implied and Historical SPD Skewness Trades Performance Kurtosis Trades Performance A Word of Caution 216

8 ix IV Econometrics Multivariate Volatility Models 221 Matthias R. Fengler and Helmut Herwartz 10.1 Introduction Model specifications Estimation of the BEKK-model An empirical illustration Data description Estimating bivariate GARCH Estimating the (co)variance processes Forecasting exchange rate densities Statistical Process Control 237 Sven Knoth 11.1 Control Charts Chart characteristics Average Run Length and Critical Values Average Delay Probability Mass and Cumulative Distribution Function Comparison with existing methods Two-sided EWMA and Lucas/Saccucci Two-sided CUSUM and Crosier Real data example - monitoring CAPM An Empirical Likelihood Goodness-of-Fit Test for Diffusions 259 Song Xi Chen, Wolfgang Härdle and Torsten Kleinow 12.1 Introduction 259

9 x 12.2 Discrete Time Approximation of a Diffusion Hypothesis Testing Kernel Estimator The Empirical Likelihood concept Introduction into Empirical Likelihood Empirical Likelihood for Time Series Data Goodness-of-Fit Statistic Goodness-of-Fit test Application Simulation Study and Illustration Appendix A simple State space model of house prices 283 Rainer Schulz and Axel Werwatz 13.1 Introduction A Statistical Model of House Prices The Price Function State Space Form Estimation with Kaiman Filter Techniques Kaiman Filtering given all parameters Filtering and State smoothing Maximum likelihood estimation of the parameters Diagnostic checking The Data Estimating and filtering in XploRe Overview Setting the System matrices 293

10 xi Kaiman filter and maximized log likelihood Diagnostic checking with standardized residuals Calculating the Kaiman smoother Appendix Procedure equivalence Smoothed constant state variables Long Memory Effects Trading Strategy 309 Oliver Jim Blaskowitz and Peter Schmidt 14.1 Introduction Hurst and Rescaled Range Analysis Stationary Long Memory Processes Fractional Brownian Motion and Noise Data Analysis Trading the Negative Persistence Locally time homogeneous time series modeling 323 Danilo Mercurio 15.1 Intervals of homogeneity The adaptive estimator A small Simulation study Estimating the coefficients of an exchange rate basket The Thai Bäht basket Estimation results Estimating the volatility of financial time series The Standard approach The locally time homogeneous approach 340

11 xii Modeling volatility via power transformation Adaptive estimation under local time-homogeneity Technical appendix Simulation based Option Pricing 349 Jens Lüssem and Jürgen Schumacher 16.1 Simulation techniques for Option pricing Introduction to Simulation techniques Pricing path independent European options on one underlying Pricing path dependent European options on one underlying Pricing options on multiple underlyings Quasi Monte Carlo (QMC) techniques for Option pricing Introduction to Quasi Monte Carlo techniques Error bounds Construction of the Haiton sequence Experimental results Pricing options with Simulation techniques - a guideline Construction of the payoff function Integration of the payoff function in the Simulation framework Restrictions for the payoff functions Nonparametric Estimators of GARCH Processes 367 Jürgen Franke, Harriet Holzberger and Marlene Müller 17.1 Deconvolution density and regression estimates Nonparametric ARMA Estimates 370

12 xiii 17.3 Nonparametric GARCH Estimates Net Based Spreadsheets in Quantitative Finance 385 Gökhan Aydmh 18.1 Introduction Client/Server based Statistical Computing Why Spreadsheets? Using MD*ReX Applications Value at Risk Calculations with Copulas Implied Volatility Measures 393 Index 398