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Applied Quantitative Finance

By: Ludger Overbeck (Editor), Wolfgang Karl Hardle (Editor), Nikolaus Hautsch (Editor)

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Hardcover | 25 August 2008 | Edition Number 2

At a Glance

Hardcover
476 Pages

Edition Type
Revised

Dimensions(cm)
23.5 x 15.5 x 2.54

Hardcover

$149.75

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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.

Industry Reviews

From the reviews of the second edition:

"The second edition ... compared with the first, has widened the scope of the overall message and topics. ... have also included more up-to-date data. ... designed for students and researchers who want to develop a professional skill in modern quantitative applications in finance. ... The aim is to make the course readable for graduate students in financial engineering but also to those who are newcomers to quantitative finance and who want to get a grip on modern statistical tools in financial data analysis." (Richard Kirby, The Mathematical Association of America, September, 2009)

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Non-Fiction Business & Management Management & Management Techniques Management Decision Making Accounting & Finance Finance Mathematics Applied Mathematics Business Mathematics & Systems Economics Econometrics Economic Statistics

Probability & Statistics

Preface to the 2nd Edition	p. v
Preface to the 1st Edition	p. vii
Contributors	p. xxi
Frequently Used Notation	p. xxv
Value at Risk	p. 1
Modeling Dependencies with Copulae	p. 3
Introduction	p. 3
Bivariate Copulae	p. 4
Copula Families	p. 6
Dependence Measures	p. 9
Multivariate Copulae	p. 11
Copula Families	p. 13
Dependence Measures	p. 15
Estimation Methods	p. 17
Goodness-of-Fit Tests for Copulae	p. 19
Simulation Methods	p. 21
Conditional Inverse Method	p. 22
Marshal-Olkin Method	p. 22
Applications to Finance	p. 23
Asset Allocation	p. 24
Value-at-Risk	p. 25
Time Series Modeling	p. 26
Simulation Study and Empirical Results	p. 28
Simulation Study	p. 28
Empirical Example	p. 30
Summary	p. 33
Quantification of Spread Risk by Means of Historical Simulation	p. 37
Introduction	p. 37
Risk Categories - a Definition of Terms	p. 37
Yield Spread Time Series	p. 39
Data Analysis	p. 40
Discussion of Results	p. 44
Historical Simulation and Value at Risk	p. 49
Risk Factor: Full Yield	p. 49
Risk Factor: Benchmark	p. 52
Risk Factor: Spread over Benchmark Yield	p. 53
Conservative Approach	p. 54
Simultaneous Simulation	p. 54
Mark-to-Model Backtesting	p. 54
VaR Estimation and Backtesting	p. 55
P-P Plots	p. 59
Q-Q Plots	p. 60
Discussion of Simulation Results	p. 60
Risk Factor: Full Yield	p. 60
Risk Factor: Benchmark	p. 61
Risk Factor: Spread over Benchmark Yield	p. 61
Conservative Approach	p. 62
Simultaneous Simulation	p. 62
Internal Risk Models	p. 63
A Copula-Based Model of the Term Structure of CDO Tranches	p. 69
Introduction	p. 69
A Copula-Based Model of Basket Credit Losses Dynamics	p. 71
Stochastic Processes with Dependent Increments	p. 72
An Algorithm for the Propagation of Losses	p. 75
Empirical Analysis	p. 76
Concluding Remarks	p. 80
VaR in High Dimensional Systems - a Conditional Correlation Approach	p. 83
Introduction	p. 83
Half-Vec Multivariate GARCH Models	p. 85
Correlation Models	p. 86
Motivation	p. 86
Log-Likelihood Decomposition	p. 87
Constant Conditional Correlation Model	p. 88
Dynamic Conditional Correlation Model	p. 89
Inference in the Correlation Models	p. 90
Generalizations of the DCC Model	p. 92
Value-at-Risk	p. 92
An Empirical Illustration	p. 93
Equal and Value Weighted Portfolios	p. 93
Estimation Results	p. 96
Credit Risk	p. 103
Rating Migrations	p. 105
Rating Transition Probabilities	p. 106
From Credit Events to Migration Counts	p. 106
Estimating Rating Transition Probabilities	p. 107
Dependent Migrations	p. 108
Computational Aspects	p. 111
Analyzing the Time-Stability of Transition Probabilities	p. 111
Aggregation over Periods	p. 111
Testing the Time-Stability of Transition Probabilities	p. 112
Example	p. 114
Computational Aspects	p. 115
Multi-Period Transitions	p. 115
Homogeneous Markov Chain	p. 116
Bootstrapping Markov Chains	p. 117
Rating Transitions of German Bank Borrowers	p. 118
Portfolio Migration	p. 119
Computational Aspects	p. 121
Cross- and Autocorrelation in Multi-Period Credit Portfolio Models	p. 125
Introduction	p. 125
The Models	p. 127
A Markov-Chain Credit Migration Model	p. 127
The Correlated-Default-Time Model	p. 130
A Discrete Barrier Model	p. 132
The Time-Changed Barrier Model	p. 133
Inter-Temporal Dependency and Autocorrelation	p. 135
Conclusion	p. 137
Risk Measurement with Spectral Capital Allocation	p. 139
Introduction	p. 139
Review of Coherent Risk Measures and Allocation	p. 140
Coherent Risk Measures	p. 140
Spectral Risk Measures	p. 143
Coherent Allocation Measures	p. 144
Spectral Allocation Measures	p. 145
Weight Function and Mixing Measure	p. 146
Risk Aversion	p. 146
Implementation	p. 147
Mixing Representation	p. 148
Density Representation	p. 149
Credit Portfolio Model	p. 149
Examples	p. 150
Weighting Scheme	p. 150
Concrete Example	p. 151
Summary	p. 158
Valuation and VaR Computation for CDOs Using Stein's Method	p. 161
Introduction	p. 161
A Primer on CDO	p. 161
Factor Models	p. 163
Numerical Algorithms	p. 164
First Order Gauss-Poisson Approximations	p. 165
Stein's Method - the Normal Case	p. 165
First-Order Gaussian Approximation	p. 167
Stein's Method - the Poisson Case	p. 171
First-Order Poisson Approximation	p. 172
Numerical Tests	p. 175
Validity Domain of the Approximations	p. 175
Stochastic Recovery Rate-Gaussian Case	p. 177
SensitivityAnalysis	p. 179
Real Life Applications	p. 180
Gaussian Approximation	p. 180
Poisson Approximation	p. 181
CDO Valuation	p. 182
Robustness of VaR Computation	p. 184
Implied Volatility	p. 191
Least Squares Kernel Smoothing of the Implied Volatility Smile	p. 193
Introduction	p. 193
Least Squares Kernel Smoothing of the Smile	p. 194
Application	p. 197
Weighting Functions, Kernels, and Minimization Scheme	p. 197
Data Description and Empirical Demonstration	p. 198
Proofs	p. 203
Numerics of Implied Binomial Trees	p. 209
Construction of the IBT	p. 210
The Derman and Kani Algorithm	p. 212
Compensation	p. 218
Barle and Cakici Algorithm	p. 219
A Simulation and a Comparison of the SPDs	p. 220
Simulation Using the DK Algorithm	p. 221
Simulation Using the BC Algorithm	p. 223
Comparison with the Monte-Carlo Simulation	p. 224
Example - Analysis of EUREX Data	p. 227
Application of Extended Kalman Filter to SPD Estimation	p. 233
Linear Model	p. 234
Linear Model for Call Option Prices	p. 235
Estimation of State Price Density	p. 236
State-Space Model for Call Option Prices	p. 237
Extended Kalman Filter and Call Options	p. 238
Empirical Results	p. 239
Extended Kalman Filtering in Practice	p. 240
SPD Estimation in 1995	p. 241
SPD Estimationin 2003	p. 243
Conclusions	p. 245
Stochastic Volatility Estimation Using Markov Chain Simulation	p. 249
The Standard Stochastic Volatility Model	p. 250
Extended SV Models	p. 252
Fat Tails and Jumps	p. 252
The Relationship Between Volatility and Returns	p. 254
The Long Memory SV Model	p. 256
MCMC-Based Bayesian Inference	p. 257
Bayes' Theorem and the MCMC Algorithm	p. 257
MCMC-Based Estimation of the Standard SV Model	p. 261
Empirical Illustrations	p. 264
The Data	p. 264
Estimation of SV Models	p. 265
Appendix	p. 270
Derivation of the Conditional Posterior Distributions	p. 270
Measuring and Modeling Risk Using High-Frequency Data	p. 275
Introduction	p. 275
Market Microstructure Effects	p. 277
Stylized Facts of Realized Volatility	p. 280
Realized Volatility Models	p. 284
Time-Varying Betas	p. 285
The Conditional CAPM	p. 286
Realized Betas	p. 287
Summary	p. 289
Valuation of Multidimensional Bermudan Options	p. 295
Introduction	p. 295
Model Assumptions	p. 296
Methodology	p. 298
Examples	p. 302
Conclusion	p. 308
Econometrics	p. 311
Multivariate Volatility Models	p. 313
Introduction	p. 313
Model Specifications	p. 314
Estimation of the BEKK-Model	p. 316
An Empirical Illustration	p. 317
Data Description	p. 317
Estimating Bivariate GARCH	p. 318
Estimating the (Co)Variance Processes	p. 320
Forecasting Exchange Rate Densities	p. 323
The Accuracy of Long-term Real Estate Valuations	p. 327
Introduction	p. 327
Implementation	p. 328
Computation of the Valuations	p. 329
Data	p. 331
Empirical Results	p. 333
Characterization of the Test Market	p. 333
Horse Race	p. 337
Conclusion	p. 343
Locally Time Homogeneous Time Series Modelling	p. 345
Introduction	p. 345
Model and Setup	p. 346
Conditional Heteroskedastic Model	p. 346
Parametric and Local Parametric Estimation and Inference	p. 347
Nearly Parametric Case	p. 348
Methods for the Estimation of Parameters	p. 349
Sequence of Intervals	p. 349
Local Change Point Selection	p. 349
Local Model Selection	p. 350
Stagewise Aggregation	p. 351
Critical Values and Other Parameters	p. 352
Applications	p. 354
Forecasting Performance for One and Multiple Steps	p. 355
Value-at-Risk	p. 357
A Multiple Time Series Example	p. 359
Simulation Based Option Pricing	p. 363
Introduction	p. 363
The Consumption Based Processes	p. 365
The Snell Envelope	p. 365
The Continuation Value, the Continuation and Exercise Regions	p. 366
Equivalence of American Options to European Ones with Consumption Processes	p. 367
Upper and Lower Bounds Using Consumption Processes	p. 367
Bermudan Options	p. 368
The Main Procedure	p. 369
Local Lower Bounds	p. 369
The Main Procedure for Constructing Upper Bounds for the Initial Position (Global Upper Bounds)	p. 370
The Main Procedure for Constructing Lower Bounds for the Initial Position (Global Lower Bounds)	p. 372
Kernel Interpolation	p. 373
Simulations	p. 374
Bermudan Max Calls on d Assets	p. 374
Bermudan Basket-Put	p. 375
Conclusions	p. 377
High-Frequency Volatility and Liquidity	p. 379
Introduction	p. 379
The Univariate MEM	p. 380
The Vector MEM	p. 383
Statistical Inference	p. 385
High-Frequency Volatility and Liquidity Dynamics	p. 387
Table of Contents provided by Publisher. All Rights Reserved.

Applied Quantitative Finance

At a Glance

Hardcover

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