Statistical Tools for Finance and Insurance (eBook)

Pavel Cizek, Wolfgang Karl Härdle, Rafał Weron (Herausgeber)

eBook Download: PDF

2011 | 2nd ed. 2011
IV, 420 Seiten
Springer Berlin (Verlag)
978-3-642-18062-0 (ISBN)

Infos

Statistical Tools for Finance and Insurance presents ready-to-use solutions, theoretical developments and method construction for many practical problems in quantitative finance and insurance. Written by practitioners and leading academics in the field, this book offers a unique combination of topics from which every market analyst and risk manager will benefit.

Features of the significantly enlarged and revised second edition:

• Offers insight into new methods and the applicability of the stochastic technology
• Provides the tools, instruments and (online) algorithms for recent techniques in quantitative finance and modern treatments in insurance calculations
• Covers topics such as
  - expected shortfall for heavy tailed and mixture distributions*
  - pricing of variance swaps*
  - volatility smile calibration in FX markets
  - pricing of catastrophe bonds and temperature derivatives*
  - building loss models and ruin probability approximation
  - insurance pricing with GLM*
  - equity linked retirement plans*(new topics in the second edition marked with*)
• Presents extensive examples

Pavel Cížek is professor of econometrics and statistics at Tilburg University. He teaches various courses covering time-series, simulation-based, and semiparametric estimation methods. His research interests are methods of semiparametric and robust statistics and econometrics with applications primarily in microeconomics and quantitative finance.

Wolfgang Karl Härdle is professor of statistics at the Humboldt-Universität zu Berlin and director of C.A.S.E. - the Centre for Applied Statistics and Economics. He teaches quantitative finance and semiparametric statistical methods. His research focuses on dynamic factor models, multivariate statistics in finance and computational statistics. He is an elected ISI member and advisor to the Guanghua School of Management, Peking University.

Rafa? Weron is professor of economics at Wroc?aw University of Technology (WUT). His research focuses on developing risk management and forecasting tools for the energy industry and computational statistics as applied to finance and insurance. He is periodically engaged as a consultant to energy (Tauron Polska Energia, Vattenfall) and financial (BRE Bank, Bank Millennium) companies. He teaches graduate level courses on energy and financial markets at NTNU (Trondheim) and WUT.

Autor

Pavel Cížek is professor of econometrics and statistics at Tilburg University. He teaches various courses covering time-series, simulation-based, and semiparametric estimation methods. His research interests are methods of semiparametric and robust statistics and econometrics with applications primarily in microeconomics and quantitative finance.Wolfgang Karl Härdle is professor of statistics at the Humboldt-Universität zu Berlin and director of C.A.S.E. – the Centre for Applied Statistics and Economics. He teaches quantitative finance and semiparametric statistical methods. His research focuses on dynamic factor models, multivariate statistics in finance and computational statistics. He is an elected ISI member and advisor to the Guanghua School of Management, Peking University.Rafał Weron is professor of economics at Wrocław University of Technology (WUT). His research focuses on developing risk management and forecasting tools for the energy industry and computational statistics as applied to finance and insurance. He is periodically engaged as a consultant to energy (Tauron Polska Energia, Vattenfall) and financial (BRE Bank, Bank Millennium) companies. He teaches graduate level courses on energy and financial markets at NTNU (Trondheim) and WUT.

Inhalt

Contents 5
Contributors 13
Preface to the second edition 15
Preface 17
Frequently used notation 21
Part I Finance 23
1 Models for heavy-tailed asset returns 24
1.1 Introduction 24
1.2 Stable distributions 25
1.2.1 Definitions and basic properties 25
1.2.2 Computation of stable density and distribution functions 28
1.2.3 Simulation of stable variables 31
1.2.4 Estimation of parameters 32
1.3 Truncated and tempered stable distributions 37
1.4 Generalized hyperbolic distributions 39
1.4.1 Definitions and basic properties 39
1.4.2 Simulation of generalized hyperbolic variables 43
1.4.3 Estimation of parameters 45
1.5 Empirical evidence 47
2. Expected shortfall 59
2.1 Introduction 59
2.2 Expected shortfall for several asymmetric, fat-tailed distributions 60
2.2.1 Expected shortfall: definitions and basic results 60
2.2.2 Student's t and extensions 62
2.2.3 ES for the stable Paretian distribution 67
2.2.4 Generalized hyperbolic and its special cases 69
2.3 Mixture distributions 72
2.3.1 Introduction 72
2.3.2 Expected shortfall for normal mixture distributions 73
2.3.3 Symmetric stable mixture 74
2.3.4 Student's t mixtures 75
2.4 Comparison study 75
2.5 Lower partial moments 78
2.6 Expected shortfall for sums 84
2.6.1 Saddlepoint approximation for density and distribution 85
2.6.2 Saddlepoint approximation for expected shortfall 86
2.6.3 Application to sums of skew normal 87
2.6.4 Application to sums of proper generalized hyperbolic 89
2.6.5 Application to sums of normal inverse Gaussian 92
2.6.6 Application to portfolio returns 94
3 Modelling conditional heteroscedasticity in nonstationary series 101
3.1 Introduction 101
3.2 Parametric conditional heteroscedasticity models 103
3.2.1 Quasi-maximum likelihood estimation 104
3.2.2 Estimation results 105
3.3 Time-varying coefficient models 108
3.3.1 Time-varying ARCH models 109
3.3.2 Estimation results 111
3.4 Pointwise adaptive estimation 114
3.4.1 Search for the longest interval of homogeneity 116
3.4.2 Choice of critical values 118
3.4.3 Estimation results 119
3.5 Adaptive weights smoothing 123
3.5.1 The AWS algorithm 124
3.5.2 Estimation results 127
3.6 Conclusion 127
4 FX smile in the Heston model 133
4.1 Introduction 133
4.2 The model 134
4.3 Option pricing 136
4.3.1 European vanilla FX option prices and Greeks 138
4.3.2 Computational issues 140
4.3.3 Behavior of the variance process and the Feller condition 142
4.3.4 Option pricing by Fourier inversion 144
4.4 Calibration 149
4.4.1 Qualitative effects of changing the parameters 149
4.4.2 The calibration scheme 150
4.4.3 Sample calibration results 152
4.5 Beyond the Heston model 155
4.5.1 Time-dependent parameters 155
4.5.2 Jump-diffusion models 158
5 Pricing of Asian temperature risk 163
5.1 The temperature derivative market 165
5.2 Temperature dynamics 167
5.3 Temperature futures pricing 170
5.3.1 CAT futures and options 171
5.3.2 CDD futures and options 173
5.3.3 Infering the market price of temperature risk 175
5.4 Asian temperature derivatives 177
5.4.1 Asian temperature dynamics 177
5.4.2 Pricing Asian futures 188
6 Variance swaps 199
6.1 Introduction 199
6.2 Volatility trading with variance swaps 200
6.3 Replication and hedging of variance swaps 201
6.4 Constructing a replication portfolio in practice 207
6.5 3G volatility products 209
6.5.1 Corridor and conditional variance swaps 211
6.5.2 Gamma swaps 212
6.6 Equity correlation (dispersion) trading with variance swaps 214
6.6.1 Idea of dispersion trading 214
6.7 Implementation of the dispersion strategy on DAX index 217
7 Learning machines to help predict bankruptcy 221
7.1 Bankruptcy analysis 222
7.2 Importance of risk classification and Basel II 233
7.3 Description of data 234
7.4 Calculations 235
7.5 Computational results 236
7.6 Conclusions 241
8 Distance matrix method for network structure analysis 246
8.1 Introduction 246
8.2 Correlation distance measures 247
8.2.1 Manhattan distance 248
8.2.2 Ultrametric distance 248
8.2.3 Noise influence on the time series distance 249
8.2.4 Manhattan distance noise influence 250
8.2.5 Ultrametric distance noise influence 252
8.2.6 Entropy distance 257
8.3 Distance matrices analysis 258
8.4 Examples 260
8.4.1 Structure of stock markets 260
8.4.2 Dynamics of the network 263
8.5 Summary 274
Part II Insurance 284
9 Building loss models 285
9.1 Introduction 285
9.2 Claim arrival processes 286
9.2.1 Homogeneous Poisson process (HPP) 287
9.2.2 Non-homogeneous Poisson process (NHPP) 289
9.2.3 Mixed Poisson process 292
9.2.4 Renewal process 293
9.3 Loss distributions 294
9.3.1 Empirical distribution function 295
9.3.2 Exponential distribution 296
9.3.3 Mixture of exponential distributions 297
9.3.4 Gamma distribution 299
9.3.5 Log-Normal distribution 301
9.3.6 Pareto distribution 303
9.3.7 Burr distribution 305
9.3.8 Weibull distribution 306
9.4 Statistical validation techniques 307
9.4.1 Mean excess function 307
9.4.2 Tests based on the empirical distribution function 310
9.5 Applications 313
9.5.1 Calibration of loss distributions 313
9.5.2 Simulation of risk processes 316
10 Ruin probability in finite time 321
10.1 Introduction 321
10.1.1 Light- and heavy-tailed distributions 323
10.2 Exact ruin probabilities in finite time 325
10.2.1 Exponential claim amounts 326
10.3 Approximations of the ruin probability in finite time 326
10.3.1 Monte Carlo method 327
10.3.2 Segerdahl normal approximation 327
10.3.3 Diffusion approximation by Brownian motion 329
10.3.4 Corrected diffusion approximation 330
10.3.5 Diffusion approximation by -stable Lévy motion 330
10.3.6 Finite time De Vylder approximation 332
10.4 Numerical comparison of the finite time approximations 334
11 Property and casualty insurance pricing with GLMs 340
11.1 Introduction 340
11.2 Insurance data used in statistical modeling 341
11.3 The structure of generalized linear models 342
11.3.1 Exponential family of distributions 343
11.3.2 The variance and link functions 344
11.3.3 The iterative algorithm 344
11.4 Modeling claim frequency 345
11.4.1 Pre-modeling steps 346
11.4.2 The Poisson model 346
11.4.3 A numerical example 347
11.5 Modeling claim severity 347
11.5.1 Data preparation 348
11.5.2 A numerical example 349
11.6 Some practical modeling issues 351
11.6.1 Non-numeric variables and banding 351
11.6.2 Functional form of the independent variables 351
11.7 Diagnosing frequency and severity models 352
11.7.1 Expected value as a function of variance 352
11.7.2 Deviance residuals 352
11.7.3 Statistical significance of the coefficients 354
11.7.4 Uniformity over time 355
11.7.5 Selecting the final models 356
11.8 Finalizing the pricing models 357
12 Pricing of catastrophe bonds 362
12.1 Introduction 362
The emergence of CAT bonds 363
Insurance securitization 365
CAT bond pricing methodology 366
12.2 Compound doubly stochastic Poisson pricing model 368
12.3 Calibration of the pricing model 370
12.4 Dynamics of the CAT bond price 372
13 Return distributions of equity-linked retirement plans 383
13.1 Introduction 383
13.2 The displaced double-exponential jump diffusion model 385
13.2.1 Model equation 385
13.2.2 Drift adjustment 388
13.2.3 Moments, variance and volatility 388
13.3 Parameter estimation 389
13.3.1 Estimating parameters from financial data 389
13.4 Interest rate curve 391
13.5 Products 391
13.5.1 Classical insurance strategy with investment in the actuarial reserve fund 391
13.5.2 Constant proportion portfolio insurance 392
13.5.3 Stop loss strategy 394
13.6 Payments to the contract and simulation horizon 395
13.7 Cost structures 396
13.8 Results without costs 397
13.9 Impact of costs 399
13.10 Impact of jumps 401
13.11 Summary 402
Index 404

Produkt-Details

• Erscheint lt. Verlag: 18.3.2011
• Zusatzinfo: IV, 420 p. 8 illus. in color.
• Verlagsort: Berlin
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Themenwelt: Wirtschaft ► Allgemeines / Lexika
• Themenwelt: Wirtschaft ► Betriebswirtschaft / Management
• Schlagworte: Catastrophe Bonds • Compound Risk Model • extreme value theory • Fuzzy Identification Model • Loss distributions • Option pricing • Quantitative Finance • Ruin Probability • Stable Distributions • Tail Dependence • VOLA Surfaces
• ISBN-10: 3-642-18062-0 / 3642180620
• ISBN-13: 978-3-642-18062-0 / 9783642180620