Applied Quantitative Finance (eBook)

Preface to the 2nd Edition 5
Preface to the 1st Edition 6
Contents 9
Contributors 18
Frequently Used Notation 21
Part I Value at Risk 23
1 Modeling Dependencies with Copulae 24
1.1 Introduction 24
1.2 Bivariate Copulae 25
1.3 Multivariate Copulae 32
1.4 Estimation Methods 38
1.5 Goodness-of-Fit Tests for Copulae 40
1.6 Simulation Methods 42
1.7 Applications to Finance 44
1.8 Simulation Study and Empirical Results 49
1.9 Summary 54
Bibliography 55
2 Quantification of Spread Risk by Means of Historical Simulation 58
2.1 Introduction 58
2.2 Risk Categories – a Definition of Terms 58
2.3 Yield Spread Time Series 60
2.4 Historical Simulation and Value at Risk 70
2.5 Mark-to-Model Backtesting 75
2.6 VaR Estimation and Backtesting 76
2.7 P-P Plots 80
2.8 Q-Q Plots 81
2.9 Discussion of Simulation Results 81
2.10 Internal Risk Models 84
Bibliography 88
3 A Copula-Based Model of the Term Structure of CDO Tranches 89
3.1 Introduction 89
3.2 A Copula-Based Model of Basket Credit Losses Dynamics 91
3.3 Stochastic Processes with Dependent Increments 92
3.4 An Algorithm for the Propagation of Losses 95
3.5 Empirical Analysis 96
3.6 Concluding Remarks 100
Bibliography 101
4 VaR in High Dimensional Systems – a Conditional Correlation Approach 102
4.1 Introduction 102
4.2 Half-Vec Multivariate GARCH Models 104
4.3 Correlation Models 105
4.4 Value-at-Risk 111
4.5 An Empirical Illustration 112
Bibliography 119
Part II Credit Risk 122
5 Rating Migrations 123
5.1 Rating Transition Probabilities 124
5.2 Analyzing the Time-Stability of Transition Probabilities 129
5.3 Multi-Period Transitions 133
Bibliography 140
6 Cross- and Autocorrelation in Multi- Period Credit Portfolio Models 142
6.1 Introduction 142
6.2 The Models 144
6.3 Inter-Temporal Dependency and Autocorrelation 152
6.4 Conclusion 154
Bibliography 155
7 Risk Measurement with Spectral Capital Allocation 156
7.1 Introduction 156
7.2 Review of Coherent Risk Measures and Allocation 157
7.3 Weight Function and Mixing Measure 163
7.4 Risk Aversion 163
7.5 Implementation 164
7.6 Credit Portfolio Model 166
7.7 Examples 167
7.8 Summary 175
Bibliography 175
8 Valuation and VaR Computation for CDOs Using Stein’s Method 177
8.1 Introduction 177
8.2 First Order Gauss-Poisson Approximations 181
8.3 Numerical Tests 191
8.4 Real Life Applications 196
Bibliography 204
Part III Implied Volatility 206
9 Least Squares Kernel Smoothing of the Implied Volatility Smile 207
9.1 Introduction 207
9.2 Least Squares Kernel Smoothing of the Smile 208
9.3 Application 211
Bibliography 216
9.4 Proofs 217
10 Numerics of Implied Binomial Trees 222
10.1 Construction of the IBT 223
10.2 A Simulation and a Comparison of the SPDs 233
10.3 Example – Analysis of EUREX Data 240
Bibliography 243
11 Application of Extended Kalman Filter to SPD Estimation 245
11.1 Linear Model 246
11.2 Extended Kalman Filter and Call Options 250
11.3 Empirical Results 251
11.4 Conclusions 257
Bibliography 258
12 Stochastic Volatility Estimation Using Markov Chain Simulation 260
12.1 The Standard Stochastic Volatility Model 261
12.2 Extended SV Models 263
12.3 MCMC-Based Bayesian Inference 268
12.4 Empirical Illustrations 275
12.5 Appendix 281
Bibliography 283
13 Measuring and Modeling Risk Using High- Frequency Data 286
13.1 Introduction 286
13.2 Market Microstructure Effects 288
13.3 Stylized Facts of Realized Volatility 291
13.4 Realized Volatility Models 295
13.5 Time-Varying Betas 296
13.6 Summary 300
Bibliography 301
14 Valuation of Multidimensional Bermudan Options 305
14.1 Introduction 305
14.2 Model Assumptions 306
14.3 Methodology 308
14.4 Examples 312
14.5 Conclusion 318
Bibliography 319
Part IV Econometrics 320
15 Multivariate Volatility Models 321
15.1 Introduction 321
15.2 An Empirical Illustration 325
15.3 Forecasting Exchange Rate Densities 331
Bibliography 333
16 The Accuracy of Long-term Real Estate Valuations 335
16.1 Introduction 335
16.2 Implementation 336
16.3 Empirical Results 341
16.4 Conclusion 351
Bibliography 351
17 Locally Time Homogeneous Time Series Modelling 353
17.1 Introduction 353
17.2 Model and Setup 354
17.3 Methods for the Estimation of Parameters 357
17.4 Critical Values and Other Parameters 360
17.5 Applications 362
Bibliography 369
18 Simulation Based Option Pricing 370
18.1 Introduction 370
18.2 The Consumption Based Processes 372
18.3 The Main Procedure 376
18.4 Simulations 381
18.5 Conclusions 384
Bibliography 385
19 High-Frequency Volatility and Liquidity 386
19.1 Introduction 386
19.2 The Univariate MEM 387
19.3 The Vector MEM 390
19.4 Statistical Inference 392
19.5 High-Frequency Volatility and Liquidity Dynamics 394
Bibliography 403
20 Statistical Process Control in Asset Management 405
20.1 Introduction 405
20.2 Review of Statistical Process Control Concepts 406
20.3 Applications of SPC in Asset Management 409
20.4 Summary 420
Bibliography 421
21 Canonical Dynamics Mechanism of Monetary Policy and Interest Rate 423
21.1 Introduction 423
21.2 Statistical Technology 425
21.3 Principles of the Fed Funds Rate Decision- Making 430
21.4 Response Curve Structure and FOMC Behavioral Analysis 434
21.5 Discussions and Conclusions 445
Bibliography 446
Index 448