QUANTITATIVE ANALYSIS IN PRACTICE
CONTENTS I VALUE AT RISK APPROXIMATING VALUE AT RISK IN CONDITIONAL GAUSSIAN MODELS INTRODUCTION THE PRACTICAL NEED STATISTICAL MODELING FOR VAR VAR APPROXIMATIONS PROS AND CONS OF DELTA-GAMMA APPROXIMATIONS GENERAL PROPERTIES OF DELTA-GAMMA-NORMAL MODELS CORNISH-FISHER APPROXIMATIONS DERIVATION PROPERTIES FOURIER INVERSION ERROR ANALYSIS TAIL BEHAVIOR INVERSION OF THE CDF MINUS THE GAUSSIAN APPROXIMATION VARIANCE REDUCTION TECHNIQUES IN MONTE-CARLO SIMULATION MONTE-CARLO SAMPLING METHOD PARTIAL MONTE-CARLO WITH IMPORTANCE SAMPLING XPLORE EXAMPLES APPLICATIONS OF COPULAS FOR THE CALCULATION OF VALUE-AT-RISK COPULAS DE?NITION SKLAR’S THEOREM EXAMPLES OF COPULAS FURTHER IMPORTANT PROPERTIES OF COPULAS COMPUTING VALUE-AT-RISK WITH COPULAS SELECTING THE MARGINAL DISTRIBUTIONS SELECTING A COPULA ESTIMATING THE COPULA PARAMETERS GENERATING SCENARIOS - MONTE CARLO VALUE-AT-RISK EXAMPLES RESULTS QUANTI?CATION OF SPREAD RISK BY MEANS OF HISTORICAL SIMULATION RISK CATEGORIES – A DE?NITION OF TERMS DESCRIPTIVE STATISTICS OF YIELD SPREAD TIME SERIES DATA ANALYSIS WITH XPLORE DISCUSSION OF RESULTS HISTORICAL SIMULATION AND VALUE AT RISK RISK FACTOR: FULL YIELD RISK FACTOR: BENCHMARK RISK FACTOR: SPREAD OVER BENCHMARK YIELD CONSERVATIVE APPROACH SIMULTANEOUS SIMULATION MARK-TO-MODEL BACKTESTING VAR ESTIMATION AND BACKTESTING WITH XPLORE P-P PLOTS Q-Q PLOTS DISCUSSION OF SIMULATION RESULTS 310 XPLORE FOR INTERNAL RISK MODELS II CREDIT RISK RATING MIGRATIONS RATING TRANSITION PROBABILITIES FROM CREDIT EVENTS TO MIGRATION COUNTS ESTIMATING RATING TRANSITION PROBABILITIES DEPENDENT MIGRATIONS COMPUTATION AND QUANTLETS ANALYZING THE TIME-STABILITY OF TRANSITION PROBABILITIES AGGREGATION OVER PERIODS ARE THE TRANSITION PROBABILITIES STATIONARY? EXAMPLES WITH GRAPHICAL PRESENTATION MULTI-PERIOD TRANSITIONS TIME HOMOGENEOUS MARKOV CHAIN BOOTSTRAPPING MARKOV CHAINS RATING TRANSITIONS OF GERMAN BANK BORROWERS PORTFOLIO MIGRATION SENSITIVITY ANALYSIS OF CREDIT PORTFOLIO MODELS CONSTRUCTION OF PORTFOLIO CREDIT RISK MODELS DEPENDENCE MODELLING FACTOR MODELLING COPULA MODELLING SIMULATIONS RANDOM SAMPLE GENERATION PORTFOLIO RESULTS III IMPLIED VOLATILITY THE ANALYSIS OF IMPLIED VOLATILITIES THE IMPLIED VOLATILITY SURFACE CALCULATING THE IMPLIED VOLATILITY SURFACE SMOOTHING DYNAMIC ANALYSIS DATA DESCRIPTION PCA OF ATM IMPLIED VOLATILITIES COMMON PCA OF THE IMPLIED VOLATILITY SURFACE HOW PRECISE ARE PRICE DISTRIBUTIONS PREDICTED BY IBT? IMPLIED BINOMIAL TREES THE DERMAN AND KANI (D & K) ALGORITHM COMPENSATION BARLE AND CAKICI (B & C) ALGORITHM A SIMULATION AND A COMPARISON OF THE SPDS SIMULATION USING DERMAN AND KANI ALGORITHM SIMULATION USING BARLE AND CAKICI ALGORITHM COMPARISON WITH MONTE-CARLO SIMULATION EXAMPLE – ANALYSIS OF DAX DATA ESTIMATING STATE-PRICE DENSITIES WITH NONPARAMETRIC REGRESSION EXTRACTING THE SPD USING CALL-OPTIONS BLACK-SCHOLES SPD SEMIPARAMETRIC ESTIMATION OF THE SPD ESTIMATING THE CALL PRICING FUNCTION FURTHER DIMENSION REDUCTION LOCAL POLYNOMIAL ESTIMATION AN EXAMPLE: APPLICATION TO DAX DATA DATA SPD, DELTA AND GAMMA BOOTSTRAP CON?DENCE BANDS COMPARISON TO IMPLIED BINOMIAL TREES TRADING ON DEVIATIONS OF IMPLIED AND HISTORICAL DENSITIES ESTIMATION OF THE OPTION IMPLIED SPD APPLICATION TO DAX DATA ESTIMATION OF THE HISTORICAL SPD THE ESTIMATION METHOD COMPARISON OF IMPLIED AND HISTORICAL SPD SKEWNESS TRADES PERFORMANCE KURTOSIS TRADES A WORD OF CAUTION IV ECONOMETRICS 10 MULTIVARIATE VOLATILITY MODELS 101 INTRODUCTION 1011 MODEL SPECI?CATIONS 1012 ESTIMATION OF THE BEKK-MODEL 102 AN EMPIRICAL ILLUSTRATION 1021 DATA DESCRIPTION 1022 ESTIMATING BIVARIATE GARCH 1023 ESTIMATING THE (CO)VARIANCE PROCESSES 103 FORECASTING EXCHANGE RATE DENSITIES 11 STATISTICAL PROCESS CONTROL 111 CONTROL CHARTS 112 CHART CHARACTERISTICS 1121 AVERAGE RUN LENGTH AND CRITICAL VALUES 1122 AVERAGE DELAY 1123 PROBABILITY MASS AND CUMULATIVE DISTRIBUTION FUNCTION 113 COMPARISON WITH EXISTING METHODS 1131 TWO-SIDED EWMA AND LUCAS/SACCUCCI 1132 TWO-SIDED CUSUM AND CROSIER 114 REAL DATA EXAMPLE – MONITORING CAPM 12 AN EMPIRICAL LIKELIHOOD GOODNESS-OF-FIT TEST FOR DI?USIONS 121 INTRODUCTION 122 DISCRETE TIME APPROXIMATION OF A DI?USION 123 HYPOTHESIS TESTING 124 KERNEL ESTIMATOR 125 THE EMPIRICAL LIKELIHOOD CONCEPT 1251 INTRODUCTION INTO EMPIRICAL LIKELIHOOD 1252 EMPIRICAL LIKELIHOOD FOR TIME SERIES DATA 126 GOODNESS-OF-FIT STATISTIC 127 GOODNESS-OF-FIT TEST 128 APPLICATION 129 SIMULATION STUDY AND ILLUSTRATION 1210APPENDIX 13 A SIMPLE STATE SPACE MODEL OF HOUSE PRICES 131 INTRODUCTION 132 A STATISTICAL MODEL OF HOUSE PRICES 1321 THE PRICE FUNCTION 1322 STATE SPACE FORM 133 ESTIMATION WITH KALMAN FILTER TECHNIQUES 1331 KALMAN FILTERING GIVEN ALL PARAMETERS 1332 FILTERING AND STATE SMOOTHING 1333 MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS 1334 DIAGNOSTIC CHECKING 134 THE DATA 135 ESTIMATING AND ?LTERING IN XPLORE 1351 OVERVIEW 1352 SETTING THE SYSTEM MATRICES 1353 KALMAN ?LTER AND MAXIMIZED LOG LIKELIHOOD 1354 DIAGNOSTIC CHECKING WITH STANDARDIZED RESIDUALS 1355 CALCULATING THE KALMAN SMOOTHER 136 APPENDIX 1361 PROCEDURE EQUIVALENCE 1362 SMOOTHED CONSTANT STATE VARIABLES 14 LONG MEMORY E?ECTS TRADING STRATEGY 141 INTRODUCTION 142 HURST AND RESCALED RANGE ANALYSIS 143 STATIONARY LONG MEMORY PROCESSES 1431 FRACTIONAL BROWNIAN MOTION AND NOISE 144 DATA ANALYSIS 145 TRADING THE NEGATIVE PERSISTENCE 15 LOCALLY TIME HOMOGENEOUS TIME SERIES MODELING 151 INTERVALS OF HOMOGENEITY 1511 THE ADAPTIVE ESTIMATOR 1512 A SMALL SIMULATION STUDY 152 ESTIMATING THE COE?CIENTS OF AN EXCHANGE RATE BASKET 1521 THE THAI BAHT BASKET 1522 ESTIMATION RESULTS 153 ESTIMATING THE VOLATILITY OF ?NANCIAL TIME SERIES 1531 THE STANDARD APPROACH 1532 THE LOCALLY TIME HOMOGENEOUS APPROACH 1533 MODELING VOLATILITY VIA POWER TRANSFORMATION 1534 ADAPTIVE ESTIMATION UNDER LOCAL TIME-HOMOGENEITY 154 TECHNICAL APPENDIX 16 SIMULATION BASED OPTION PRICING 161 SIMULATION TECHNIQUES FOR OPTION PRICING 1611 INTRODUCTION TO SIMULATION TECHNIQUES 1612 PRICING PATH INDEPENDENT EUROPEAN OPTIONS ON ONE UN- DERLYING 1613 PRICING PATH DEPENDENT EUROPEAN OPTIONS ON ONE UNDER- LYING 1614 PRICING OPTIONS ON MULTIPLE UNDERLYINGS 162 QUASI MONTE CARLO (QMC) TECHNIQUES FOR OPTION PRICING 1621 INTRODUCTION TO QUASI MONTE CARLO TECHNIQUES 1622 ERROR BOUNDS 1623 CONSTRUCTION OF THE HALTON SEQUENCE 1624 EXPERIMENTAL RESULTS 163 PRICING OPTIONS WITH SIMULATION TECHNIQUES - A GUIDELINE 1631 CONSTRUCTION OF THE PAYO?FUNCTION 1632 INTEGRATION OF THE PAYO?FUNCTION IN THE SIMULATION FRAME- WORK 1633 RESTRICTIONS FOR THE PAYO?FUNCTIONS 17 NONPARAMETRIC ESTIMATORS OF GARCH PROCESSES J¨URGEN FRANKE, HARRIET HOLZBERGER AND MARLENE M¨ULLER 171 DECONVOLUTION DENSITY AND REGRESSION ESTIMATES 172 NONPARAMETRIC ARMA ESTIMATES 173 NONPARAMETRIC GARCH ESTIMATES 18 NET BASED SPREADSHEETS IN QUANTITATIVE FINANCE 181 INTRODUCTION 182 CLIENT/SERVER BASED STATISTICAL COMPUTING 183 WHY SPREADSHEETS? 184 USING MD*REX 185 APPLICATIONS 1851 VALUE AT RISK CALCULATIONS WITH COPULAS 1852 IMPLIED VOLATILITY MEASURES