Authors: Jurgen Franke, ChristianM.Hafner, and Wolfgang K. Hardle

part contents:
14 Non-parametric Concepts for Financial Time Series 279
14.1 Nonparametric Regression . . . . . . . . . . . . . . . . . . . . 280
14.2 Construction of the Estimator . . . . . . . . . . . . . . . . . . 283
14.3 Asymptotic Normality . . . . . . . . . . . . . . . . . . . . . . 286
14.4 Recommended Literature . . . . . . . . . . . . . . . . . . . . 301
15 Pricing Options with Flexible Volatility Estimators
15.1 Pricing Options with ARCH-Models . . . . . . . . . . . . . . 305
15.2 AMonte Carlo Study . . . . . . . . . . . . . . . . . . . . . . 312
15.3 Application to the Valuation of DAX Calls . . . . . . . . . . 315
15.4 Recommended Literature . . . . . . . . . . . . . . . . . . . . 319
17 Copulae and Value at Risk 333
17.2 Copula Estimation . . . . . . . . . . . . . . . . . . . . . . . . 349
17.2.1 Maximum Likelihood Estimation . . . . . . . . . . . . 351
17.2.2 IFM- Inference for Margins . . . . . . . . . . . . . . . 351
17.2.3 CML - Canonical Maximum Likelihood . . . . . . . . 351
17.2.4 Gaussian Copula Estimation . . . . . . . . . . . . . . 352
17.2.5 t-Copula Estimation . . . . . . . . . . . . . . . . . . . 353
17.3 Value-at-Risk and Copulae . . . . . . . . . . . . . . . . . . . 354
17.4 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . 356
18 Statistics of Extreme Risks 371
18.1 Limit Behaviour of Maxima . . . . . . . . . . . . . . . . . . . 371
18.2 Statistics of Extreme Events . . . . . . . . . . . . . . . . . . . 380
18.3 Estimators for RiskMeasurements . . . . . . . . . . . . . . . 390
18.4 Extreme Value Theory for Time Series . . . . . . . . . . . . . 392
18.5 Recommended Literature . . . . . . . . . . . . . . . . . . . . 396
19 Neural Networks 399
21 Nonparametric Estimators for the Probability of Default 443
21.1 Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . 443
21.2 Semi-parametricModel for Credit Rating . . . . . . . . . . . 445
21.3 Credit Ratings with Neural Networks . . . . . . . . . . . . . . 449