Applied Quantitative Finance : Theory and Computational Tools

by Hardle, Wolfgang; Hardle, Wolfgang; Kleinow, T.; Kleinow, T.; Stahl, Gerhard

• ISBN13: 9783540434603
• ISBN10: 3540434607
• Format: Paperback
• Copyright: 2002-12-01
• Publisher: Springer Verlag

Summary

Applied Quantitative Financepresents solutions, theoretical developments and method proliferation for many practical problems in quantitative finance. The combination of practice and theory supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on the practical implementation and theoretical concepts. This concept offers theoreticians insight into the applicability of the methodology and, vice versa, practitioners access to new methods for their applications. The e-book design of the text links theory and computational tools in an innovative way. All "quantlets" for the calculation of given examples in the text are executable on an XploRe Quantlet Server (XQS) and can be modified by the reader via the internet. The electronic edition can be downloaded from the web site www.i-xplore.de using the licence and registration number at the back cover.

Table of Contents

Preface	p. xv
Contributors	p. xix
Frequently Used Notation	p. xxi
Value at Risk	p. 1
Approximating Value at Risk in Conditional Gaussian Models	p. 3
Introduction	p. 3
The Practical Need	p. 3
Statistical Modeling for VaR	p. 4
VaR Approximations	p. 6
Pros and Cons of Delta-Gamma Approximations	p. 7
General Properties of Delta-Gamma-Normal Models	p. 8
Cornish-Fisher Approximations	p. 12
Derivation	p. 12
Properties	p. 15
Fourier Inversion	p. 16
Error Analysis	p. 16
Tail Behavior	p. 20
Inversion of the cdf minus the Gaussian Approximation	p. 21
Variance Reduction Techniques in Monte-Carlo Simulation	p. 24
Monte-Carlo Sampling Method	p. 24
Partial Monte-Carlo with Importance Sampling	p. 28
XploRe Examples	p. 30
Applications of Copulas for the Calculation of Value-at-Risk	p. 35
Copulas	p. 36
Definition	p. 36
Sklar's Theorem	p. 37
Examples of Copulas	p. 37
Further Important Properties of Copulas	p. 39
Computing Value-at-Risk with Copulas	p. 40
Selecting the Marginal Distributions	p. 40
Selecting a Copula	p. 41
Estimating the Copula Parameters	p. 41
Generating Scenarios - Monte Carlo Value-at-Risk	p. 43
Examples	p. 45
Results	p. 47
Quantification of Spread Risk by Means of Historical Simulation	p. 51
Introduction	p. 51
Risk Categories - a Definition of Terms	p. 51
Descriptive Statistics of Yield Spread Time Series	p. 53
Data Analysis with XploRe	p. 54
Discussion of Results	p. 58
Historical Simulation and Value at Risk	p. 63
Risk Factor: Full Yield	p. 64
Risk Factor: Benchmark	p. 67
Risk Factor: Spread over Benchmark Yield	p. 68
Conservative Approach	p. 69
Simultaneous Simulation	p. 69
Mark-to-Model Backtesting	p. 70
VaR Estimation and Backtesting with XploRe	p. 70
P-P Plots	p. 73
Q-Q Plots	p. 74
Discussion of Simulation Results	p. 75
Risk Factor: Full Yield	p. 77
Risk Factor: Benchmark	p. 78
Risk Factor: Spread over Benchmark Yield	p. 78
Conservative Approach	p. 79
Simultaneous Simulation	p. 80
XploRe for Internal Risk Models	p. 81
Credit Risk	p. 85
Rating Migrations	p. 87
Rating Transition Probabilities	p. 88
From Credit Events to Migration Counts	p. 88
Estimating Rating Transition Probabilities	p. 89
Dependent Migrations	p. 90
Computation and Quantlets	p. 93
Analyzing the Time-Stability of Transition Probabilities	p. 94
Aggregation over Periods	p. 94
Are the Transition Probabilities Stationary?	p. 95
Computation and Quantlets	p. 97
Examples with Graphical Presentation	p. 98
Multi-Period Transitions	p. 101
Time Homogeneous Markov Chain	p. 101
Bootstrapping Markov Chains	p. 102
Computation and Quantlets	p. 104
Rating Transitions of German Bank Borrowers	p. 106
Portfolio Migration	p. 106
Sensitivity analysis of credit portfolio models	p. 111
Introduction	p. 111
Construction of portfolio credit risk models	p. 113
Dependence modelling	p. 114
Factor modelling	p. 115
Copula modelling	p. 117
Simulations	p. 119
Random sample generation	p. 119
Portfolio results	p. 120
Implied Volatility	p. 125
The Analysis of Implied Volatilities	p. 127
Introduction	p. 128
The Implied Volatility Surface	p. 129
Calculating the Implied Volatility	p. 129
Surface smoothing	p. 131
Dynamic Analysis	p. 134
Data description	p. 134
PCA of ATM Implied Volatilities	p. 136
Common PCA of the Implied Volatility Surface	p. 137
How Precise Are Price Distributions Predicted by IBT?	p. 145
Implied Binomial Trees	p. 146
The Derman and Kani (D & K) algorithm	p. 147
Compensation	p. 151
Barle and Cakici (B & C) algorithm	p. 153
A Simulation and a Comparison of the SPDs	p. 154
Simulation using Derman and Kani algorithm	p. 154
Simulation using Barle and Cakici algorithm	p. 156
Comparison with Monte-Carlo Simulation	p. 158
Example - Analysis of DAX data	p. 162
Estimating State-Price Densities with Nonparametric Regression	p. 171
Introduction	p. 171
Extracting the SPD using Call-Options	p. 173
Black-Scholes SPD	p. 175
Semiparametric estimation of the SPD	p. 176
Estimating the call pricing function	p. 176
Further dimension reduction	p. 177
Local Polynomial Estimation	p. 181
An Example: Application to DAX data	p. 183
Data	p. 183
SPD, delta and gamma	p. 185
Bootstrap confidence bands	p. 187
Comparison to Implied Binomial Trees	p. 190
Trading on Deviations of Implied and Historical Densities	p. 197
Introduction	p. 197
Estimation of the Option Implied SPD	p. 198
Application to DAX Data	p. 198
Estimation of the Historical SPD	p. 200
The Estimation Method	p. 201
Application to DAX Data	p. 202
Comparison of Implied and Historical SPD	p. 205
Skewness Trades	p. 207
Performance	p. 210
Kurtosis Trades	p. 212
Performance	p. 214
A Word of Caution	p. 216
Econometrics	p. 219
Multivariate Volatility Models	p. 221
Introduction	p. 221
Model specifications	p. 222
Estimation of the BEKK-model	p. 224
An empirical illustration	p. 225
Data description	p. 225
Estimating bivariate GARCH	p. 226
Estimating the (co)variance processes	p. 229
Forecasting exchange rate densities	p. 232
Statistical Process Control	p. 237
Control Charts	p. 238
Chart characteristics	p. 243
Average Run Length and Critical Values	p. 247
Average Delay	p. 248
Probability Mass and Cumulative Distribution Function	p. 248
Comparison with existing methods	p. 251
Two-sided EWMA and Lucas/Saccucci	p. 251
Two-sided CUSUM and Crosier	p. 251
Real data example - monitoring CAPM	p. 253
An Empirical Likelihood Goodness-of-Fit Test for Diffusions	p. 259
Introduction	p. 259
Discrete Time Approximation of a Diffusion	p. 260
Hypothesis Testing	p. 261
Kernel Estimator	p. 263
The Empirical Likelihood concept	p. 264
Introduction into Empirical Likelihood	p. 264
Empirical Likelihood for Time Series Data	p. 265
Goodness-of-Fit Statistic	p. 268
Goodness-of-Fit test	p. 272
Application	p. 274
Simulation Study and Illustration	p. 276
Appendix	p. 279
A simple state space model of house prices	p. 283
Introduction	p. 283
A Statistical Model of House Prices	p. 284
The Price Function	p. 284
State Space Form	p. 285
Estimation with Kalman Filter Techniques	p. 286
Kalman Filtering given all parameters	p. 286
Filtering and state smoothing	p. 287
Maximum likelihood estimation of the parameters	p. 288
Diagnostic checking	p. 289
The Data	p. 289
Estimating and filtering in XploRe	p. 293
Overview	p. 293
Setting the system matrices	p. 293
Kalman filter and maximized log likelihood	p. 295
Diagnostic checking with standardized residuals	p. 298
Calculating the Kalman smoother	p. 300
Appendix	p. 302
Procedure equivalence	p. 302
Smoothed constant state variables	p. 304
Long Memory Effects Trading Strategy	p. 309
Introduction	p. 309
Hurst and Rescaled Range Analysis	p. 310
Stationary Long Memory Processes	p. 312
Fractional Brownian Motion and Noise	p. 313
Data Analysis	p. 315
Trading the Negative Persistence	p. 318
Locally time homogeneous time series modeling	p. 323
Intervals of homogeneity	p. 323
The adaptive estimator	p. 326
A small simulation study	p. 327
Estimating the coefficients of an exchange rate basket	p. 329
The Thai Baht basket	p. 331
Estimation results	p. 335
Estimating the volatility of financial time series	p. 338
The standard approach	p. 339
The locally time homogeneous approach	p. 340
Modeling volatility via power transformation	p. 340
Adaptive estimation under local time-homogeneity	p. 341
Technical appendix	p. 344
Simulation based Option Pricing	p. 349
Simulation techniques for option pricing	p. 349
Introduction to simulation techniques	p. 349
Pricing path independent European options on one underlying	p. 350
Pricing path dependent European options on one underlying	p. 354
Pricing options on multiple underlyings	p. 355
Quasi Monte Carlo (QMC) techniques for option pricing	p. 356
Introduction to Quasi Monte Carlo techniques	p. 356
Error bounds	p. 356
Construction of the Halton sequence	p. 357
Experimental results	p. 359
Pricing options with simulation techniques - a guideline	p. 361
Construction of the payoff function	p. 362
Integration of the payoff function in the simulation framework	p. 362
Restrictions for the payoff functions	p. 365
Nonparametric Estimators of GARCH Processes	p. 367
Deconvolution density and regression estimates	p. 369
Nonparametric ARMA Estimates	p. 370
Nonparametric GARCH Estimates	p. 379
Net Based Spreadsheets in Quantitative Finance	p. 385
Introduction	p. 385
Client/Server based Statistical Computing	p. 386
Why Spreadsheets?	p. 387
Using MD*ReX	p. 388
Applications	p. 390
Value at Risk Calculations with Copulas	p. 391
Implied Volatility Measures	p. 393
Index	p. 398
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