[Book] Mathematics of Financial Modeling and Investment Management - Fabozzi, Frank

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THE MATHEMATICS OF FINANCIAL MODELING & INVESTMENT MANAGEMENT THE MATHEMATICS OF FINANCIAL MODELING & INVESTMENT MANAGEMENT COVERS A WIDE RANGE OF TECHNICAL TOPICS IN MATHEMATICS AND FINANCE?ENABLING THE INVESTMENT MANAGEMENT PRACTITIONER, RESEARCHER, OR STUDENT TO FULLY UNDERSTAND THE PROCESS OF FINANCIAL DECISION-MAKING AND ITS ECONOMIC FOUNDATIONS. THIS COMPREHENSIVE RESOURCE WILL INTRODUCE YOU TO KEY MATHEMATICAL TECHNIQUES?MATRIX ALGEBRA, CALCULUS, ORDINARY DIFFERENTIAL EQUATIONS, PROBABILITY THEORY, STOCHASTIC CALCULUS, TIME SERIES ANALYSIS, OPTIMIZATION?AS WELL AS SHOW YOU HOW THESE TECHNIQUES ARE SUCCESSFULLY IMPLEMENTED IN THE WORLD OF MODERN FINANCE. SPECIAL EMPHASIS IS PLACED ON THE NEW MATHEMATICAL TOOLS THAT ALLOW A DEEPER UNDERSTANDING OF FINANCIAL ECONOMETRICS AND FINANCIAL ECONOMICS. RECENT ADVANCES IN FINANCIAL ECONOMETRICS, SUCH AS TOOLS FOR ESTIMATING AND REPRESENTING THE TAILS OF THE DISTRIBUTIONS, THE ANALYSIS OF CORRELATION PHENOMENA, AND DIMENSIONALITY REDUCTION THROUGH FACTOR ANALYSIS AND COINTEGRATION ARE DISCUSSED IN DEPTH. USING A WEALTH OF REAL-WORLD EXAMPLES, FOCARDI AND FABOZZI SIMULTANEOUSLY SHOW BOTH THE MATHEMATICAL TECHNIQUES AND THE AREAS IN FINANCE WHERE THESE TECHNIQUES ARE APPLIED. THEY ALSO COVER A VARIETY OF USEFUL FINANCIAL APPLICATIONS, SUCH AS: ARBITRAGE PRICING INTEREST RATE MODELING DERIVATIVE PRICING CREDIT RISK MODELING EQUITY AND BOND PORTFOLIO MANAGEMENT RISK MANAGEMENT AND MUCH MORE FILLED WITH IN-DEPTH INSIGHT AND EXPERT ADVICE, THE MATHEMATICS OF FINANCIAL MODELING & INVESTMENT MANAGEMENT CLEARLY TIES TOGETHER FINANCIAL THEORY AND MATHEMATICAL TECHNIQUES. AUTHOR BIOGRAPHY: SERGIO FOCARDI IS A FOUNDING PARTNER OF THE INTERTEK GROUP, A PARIS-BASED FIRM PROVIDING CONSULTING ON ADVANCED MATHEMATICAL METHODS IN BANKING AND FINANCE, AND A COFOUNDER OF CINEF (CENTER FOR INTERDISCIPLINARY RESEARCH IN ECONOMICS AND FINANCE) AT THE UNIVERSITY OF GENOA, ITALY. FOCARDI’S RESEARCH INTERESTS FOCUS ON STATISTICAL ARBITRAGE, DYNAMIC FACTOR ANALYSIS, AND FINANCIAL MODELING IN A MULTIPLE HETEROGENEOUS INTERACTING AGENTS FRAMEWORK. HE HAS PUBLISHED NUMEROUS ARTICLES AND COAUTHORED THE BOOKS MODELING THE MARKET: NEW THEORIES AND TECHNIQUES AND RISK MANAGEMENT: FRAMEWORK, METHODS, AND PRACTICE (BOTH PUBLISHED BY WILEY). FOCARDI HOLDS A DEGREE IN ELECTRONIC ENGINEERING FROM THE UNIVERSITY OF GENOA. FRANK J. FABOZZI, PHD, CFA, IS THE FREDERICK FRANK ADJUNCT PROFESSOR OF FINANCE AT YALE UNIVERSITY’S SCHOOL OF MANAGEMENT AND EDITOR OF THE JOURNAL OF PORTFOLIO MANAGEMENT. FABOZZI IS A CHARTERED FINANCIAL ANALYST AND CERTIFIED PUBLIC ACCOUNTANT WHO HAS AUTHORED AND EDITED MANY ACCLAIMED BOOKS IN FINANCE. HE EARNED A DOCTORATE IN ECONOMICS FROM THE CITY UNIVERSITY OF NEW YORK IN 1972. HE IS A FELLOW OF THE INTERNATIONAL CENTER FOR FINANCE AT YALE UNIVERSITY. -FROM THE PUBLISHER [인터넷 교보문고 제공]

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PREFACE XIV ACKNOWLEDGMENTS XVI ABOUT THE AUTHORS XVIII COMMONLY USED SYMBOLS XIX ABBREVIATIONS AND ACRONYMS XX FROM ART TO ENGINEERING IN FINANCE 1(20) INVESTMENT MANAGEMENT PROCESS 2(8) STEP 1: SETTING INVESTMENT OBJECTIVES 2(1) STEP 2: ESTABLISHING AN INVESTMENT POLICY 2(4) STEP 3: SELECTING A PORTFOLIO STRATEGY 6(1) STEP 4: SELECTING THE SPECIFIC ASSETS 7(2) STEP 5: MEASURING AND EVALUATING PERFORMANCE 9(1) FINANCIAL ENGINEERING IN HISTORICAL PERSPECTIVE 10(1) THE ROLE OF INFORMATION TECHNOLOGY 11(2) INDUSTRY'S EVALUATION OF MODELING TOOLS 13(2) INTEGRATING QUALITATIVE AND QUANTITATIVE INFORMATION 15(2) PRINCIPLES FOR ENGINEERING A SUITE OF MODELS 17(1) SUMMARY 18(3) OVERVIEW OF FINANCIAL MARKETS, FINANCIAL ASSETS, AND MARKET PARTICIPANTS 21(54) FINANCIAL ASSETS 21(4) FINANCIAL MARKETS 25(9) CLASSIFICATION OF FINANCIAL MARKETS 25(1) ECONOMIC FUNCTIONS OF FINANCIAL MARKETS 26(1) SECONDARY MARKETS 27(7) OVERVIEW OF MARKET PARTICIPANTS 34(11) ROLE OF FINANCIAL INTERMEDIARIES 35(2) INSTITUTIONAL INVESTORS 37(4) INSURANCE COMPANIES 41(1) PENSION FUNDS 41(1) INVESTMENT COMPANIES 42(1) DEPOSITORY INSTITUTIONS 43(2) ENDOWMENTS AND FOUNDATIONS 45(1) COMMON STOCK 45(6) TRADING LOCATIONS 45(1) STOCK MARKET INDICATORS 46(2) TRADING ARRANGEMENTS 48(3) BONDS 51(6) MATURITY 51(1) PAR VALUE 52(1) COUPON RATE 52(3) PROVISIONS FOR PAYING OFF BONDS 55(1) OPTIONS GRANTED TO BONDHOLDERS 56(1) FUTURES AND FORWARD CONTRACTS 57(7) FUTURES VERSUS FORWARD CONTRACTS 58(1) RISK AND RETURN CHARACTERISTICS OF FUTURES CONTRACTS 59(1) PRICING OF FUTURES CONTRACTS 59(4) THE ROLE OF FUTURES IN FINANCIAL MARKETS 63(1) OPTIONS 64(5) RISK-RETURN FOR OPTIONS 66(1) THE OPTION PRICE 66(3) SWAPS 69(1) CAPS AND FLOORS 70(1) SUMMARY 71(4) MILESTONES IN FINANCIAL MODELING AND INVESTMENT MANAGEMENT 75(16) THE PRECURSORS: PARETO, WALRAS, AND THE LAUSANNE SCHOOL 76(2) PRICE DIFFUSION: BACHELIER 78(2) THE RUIN PROBLEM IN INSURANCE: LUNDBERG 80(1) THE PRINCIPLES OF INVESTMENT: MARKOWITZ 81(2) UNDERSTANDING VALUE: MODIGLIANI AND MILLER 83(2) MODIGLIANI-MILLER IRRELEVANCE THEOREMS AND THE ABSENCE OF ARBITRAGE 84(1) EFFICIENT MARKETS: FAMA AND SAMUELSON 85(1) CAPITAL ASSET PRICING MODEL: SHARPE, LINTNER, AND MOSSIN 86(1) THE MULTIFACTOR CAPM: MERTON 87(1) ARBITRAGE PRICING THEORY: ROSS 88(1) ARBITRAGE, HEDGING, AND OPTION THEORY: BLACK, SCHOLES, AND MERTON 89(1) SUMMARY 90(1) PRINCIPLES OF CALCULUS 91(50) SETS AND SET OPERATIONS 93(3) PROPER SUBSETS 93(2) EMPTY SETS 95(1) UNION OF SETS 95(1) INTERSECTION OF SETS 95(1) ELEMENTARY PROPERTIES OF SETS 96(1) DISTANCES AND QUANTITIES 96(4) N-TUPLES 97(1) DISTANCE 98(1) DENSITY OF POINTS 99(1) FUNCTIONS 100(1) VARIABLES 101(1) LIMITS 102(1) CONTINUITY 103(2) TOTAL VARIATION 105(1) DIFFERENTIATION 106(5) COMMONLY USED RULES FOR COMPUTING DERIVATIVES 107(4) HIGHER ORDER DERIVATIVES 111(10) APPLICATION TO BOND ANALYSIS 112(9) TAYLOR SERIES EXPANSION 121(6) APPLICATION TO BOND ANALYSIS 122(5) INTEGRATION 127(4) RIEMANN INTEGRALS 127(2) PROPERTIES OF RIEMANN INTEGRALS 129(1) LEBESQUE-STIELTJES INTEGRALS 130(1) INDEFINITE AND IMPROPER INTEGRALS 131(1) THE FUNDAMENTAL THEOREM OF CALCULUS 132(2) INTEGRAL TRANSFORMS 134(4) LAPLACE TRANSFORMS 134(3) FOURIER TRANSFORMS 137(1) CALCULUS IN MORE THAN ONE VARIABLE 138(1) SUMMARY 139(2) MATRIX ALGEBRA 141(24) VECTORS AND MATRICES DEFINED 141(4) VECTORS 141(3) MATRICES 144(1) SQUARE MATRICES 145(3) DIAGONALS AND ANTIDIAGONALS 145(1) IDENTITY MATRIX 146(1) DIAGONAL MATRIX 146(2) UPPER AND LOWER TRIANGULAR MATRIX 148(1) DETERMINANTS 148(1) SYSTEMS OF LINEAR EQUATIONS 149(2) LINEAR INDEPENDENCE AND RANK 151(1) HANKEL MATRIX 152(1) VECTOR AND MATRIX OPERATIONS 153(7) VECTOR OPERATIONS 153(3) MATRIX OPERATIONS 156(4) EIGENVALUES AND EIGENVECTORS 160(1) DIAGONALIZATION AND SIMILARITY 161(1) SINGULAR VALUE DECOMPOSITION 162(1) SUMMARY 163(2) CONCEPTS OF PROBABILITY 165(36) REPRESENTING UNCERTAINTY WITH MATHEMATICS 165(2) PROBABILITY IN A NUTSHELL 167(2) OUTCOMES AND EVENTS 169(1) PROBABILITY 170(1) MEASURE 171(1) RANDOM VARIABLES 172(1) INTEGRALS 172(2) DISTRIBUTIONS AND DISTRIBUTION FUNCTIONS 174(1) RANDOM VECTORS 175(3) STOCHASTIC PROCESSES 178(2) PROBABILISTIC REPRESENTATION OF FINANCIAL MARKETS 180(1) INFORMATION STRUCTURES 181(1) FILTRATION 182(2) CONDITIONAL PROBABILITY AND CONDITIONAL EXPECTATION 184(2) MOMENTS AND CORRELATION 186(2) COPULA FUNCTIONS 188(1) SEQUENCES OF RANDOM VARIABLES 189(2) INDEPENDENT AND IDENTICALLY DISTRIBUTED SEQUENCES 191(1) SUM OF VARIABLES 191(3) GAUSSIAN VARIABLES 194(3) THE REGRESSION FUNCTION 197(2) LINEAR REGRESSION 197(2) SUMMARY 199(2) OPTIMIZATION 201(16) MAXIMA AND MINIMA 202(2) LAGRANGE MULTIPLIERS 204(2) NUMERICAL ALGORITHMS 206(6) LINEAR PROGRAMMING 206(5) QUADRATIC PROGRAMMING 211(1) CALCULUS OF VARIATIONS AND OPTIMAL CONTROL THEORY 212(2) STOCHASTIC PROGRAMMING 214(2) SUMMARY 216(1) STOCHASTIC INTEGRALS 217(22) THE INTUITION BEHIND STOCHASTIC INTEGRALS 219(6) BROWNIAN MOTION DEFINED 225(5) PROPERTIES OF BROWNIAN MOTION 230(2) STOCHASTIC INTEGRALS DEFINED 232(4) SOME PROPERTIES OF ITO STOCHASTIC INTEGRALS 236(1) SUMMARY 237(2) DIFFERENTIAL EQUATIONS AND DIFFERENCE EQUATIONS 239(28) DIFFERENTIAL EQUATIONS DEFINED 240(1) ORDINARY DIFFERENTIAL EQUATIONS 240(3) ORDER AND DEGREE OF AN ODE 241(1) SOLUTION TO AN ODE 241(2) SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS 243(3) CLOSED-FORM SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 246(3) LINEAR DIFFERENTIAL EQUATIONS 247(2) NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS 249(7) THE FINITE DIFFERENCE METHOD 249(7) NONLINEAR DYNAMICS AND CHAOS 256(3) FRACTALS 258(1) PARTIAL DIFFERENTIAL EQUATIONS 259(6) DIFFUSION EQUATION 259(2) SOLUTION OF THE DIFFUSION EQUATION 261(2) NUMERICAL SOLUTION OF PDES 263(2) SUMMARY 265(2) STOCHASTIC DIFFERENTIAL EQUATIONS 267(16) THE INTUITION BEHIND STOCHASTIC DIFFERENTIAL EQUATIONS 268(3) ITO PROCESSES 271(1) THE 1-DIMENSIONAL ITO FORMULA 272(2) STOCHASTIC DIFFERENTIAL EQUATIONS 274(2) GENERALIZATION TO SEVERAL DIMENSIONS 276(2) SOLUTION OF STOCHASTIC DIFFERENTIAL EQUATIONS 278(4) THE ARITHMETIC BROWNIAN MOTION 280(1) THE ORNSTEIN-UHLENBECK PROCESS 280(1) THE GEOMETRIC BROWNIAN MOTION 281(1) SUMMARY 282(1) FINANCIAL ECONOMETRICS: TIME SERIES CONCEPTS, REPRESENTATIONS, AND MODELS 283(32) CONCEPTS OF TIME SERIES 284(2) STYLIZED FACTS OF FINANCIAL TIME SERIES 286(2) INFINITE MOVING-AVERAGE AND AUTOREGRESSIVE REPRESENTATION OF TIME SERIES 288(9) UNIVARIATE STATIONARY SERIES 288(1) THE LAG OPERATOR L 289(3) STATIONARY UNIVARIATE MOVING AVERAGE 292(1) MULTIVARIATE STATIONARY SERIES 293(2) NONSTATIONARY SERIES 295(2) ARMA REPRESENTATIONS 297(8) STATIONARY UNIVARIATE ARMA MODELS 297(3) NONSTATIONARY UNIVARIATE ARMA MODELS 300(1) STATIONARY MULTIVARIATE ARMA MODELS 301(3) NONSTATIONARY MULTIVARIATE ARMA MODELS 304(1) MARKOV COEFFICIENTS AND ARMA MODELS 304(1) HANKEL MATRICES AND ARMA MODELS 305(1) STATE-SPACE REPRESENTATION 305(4) EQUIVALENCE OF STATE-SPACE AND ARMA REPRESENTATIONS 308(1) INTEGRATED SERIES AND TRENDS 309(4) SUMMARY 313(2) FINANCIAL ECONOMETRICS: MODEL SELECTION, ESTIMATION, AND TESTING 315(36) MODEL SELECTION 315(2) LEARNING AND MODEL COMPLEXITY 317(2) MAXIMUM LIKELIHOOD ESTIMATE 319(5) LINEAR MODELS OF FINANCIAL TIME SERIES 324(1) RANDOM WALK MODELS 324(3) CORRELATION 327(2) RANDOM MATRICES 329(3) MULTIFACTOR MODELS 332(6) CAPM 334(1) ASSET PRICING THEORY (APT) MODELS 335(1) PCA AND FACTOR MODELS 335(3) VECTOR AUTOREGRESSIVE MODELS 338(1) COINTEGRATION 339(6) STATE-SPACE MODELING AND COINTEGRATION 342(1) EMPIRICAL EVIDENCE OF COINTEGRATION IN EQUITY PRICES 343(2) NONSTATIONARY MODELS OF FINANCIAL TIME SERIES 345(4) THE ARCH/GARCH FAMILY OF MODELS 346(1) MARKOV SWITCHING MODELS 347(2) SUMMARY 349(2) FAT TAILS, SCALING, AND STABLE LAWS 351(42) SCALING, STABLE LAWS, AND FAT TAILS 352(10) FAT TAILS 352(1) THE CLASS ? OF FAT-TAILED DISTRIBUTIONS 353(5) THE LAW OF LARGE NUMBERS AND THE CENTRAL LIMIT THEOREM 358(2) STABLE DISTRIBUTIONS 360(2) EXTREME VALUE THEORY FOR IID PROCESSES 362(16) MAXIMA 362(6) MAX-STABLE DISTRIBUTIONS 368(1) GENERALIZED EXTREME VALUE DISTRIBUTIONS 368(1) ORDER STATISTICS 369(2) POINT PROCESS OF EXCEEDANCES OR PEAKS OVER THRESHOLD 371(2) ESTIMATION 373(5) ELIMINATING THE ASSUMPTION OF IID SEQUENCES 378(10) HEAVY-TAILED ARMA PROCESSES 381(1) ARCH/GARCH PROCESSES 382(1) SUBORDINATED PROCESSES 383(1) MARKOV SWITCHING MODELS 384(1) ESTIMATION 384(1) SCALING AND SELF-SIMILARITY 385(3) EVIDENCE OF FAT TAILS IN FINANCIAL VARIABLES 388(3) ON THE APPLICABILITY OF EXTREME VALUE THEORY IN FINANCE 391(1) SUMMARY 392(1) ARBITRAGE PRICING: FINITE-STATE MODELS 393(48) THE ARBITRAGE PRINCIPLE 393(2) ARBITRAGE PRICING IN A ONE-PERIOD SETTING 395(7) STATE PRICES 397(1) RISK-NEUTRAL PROBABILITIES 398(1) COMPLETE MARKETS 399(3) ARBITRAGE PRICING IN A MULTIPERIOD FINITE-STATE SETTING 402(21) PROPAGATION OF INFORMATION 402(1) TRADING STRATEGIES 403(1) STATE-PRICE DEFLATOR 404(1) PRICING RELATIONSHIPS 405(9) EQUIVALENT MARTINGALE MEASURES 414(2) RISK-NEUTRAL PROBABILITIES 416(7) PATH DEPENDENCE AND MARKOV MODELS 423(1) THE BINOMIAL MODEL 423(4) RISK-NEUTRAL PROBABILITIES FOR THE BINOMIAL MODEL 426(1) VALUATION OF EUROPEAN SIMPLE DERIVATIVES 427(2) VALUATION OF AMERICAN OPTIONS 429(1) ARBITRAGE PRICING IN A DISCRETE-TIME, CONTINUOUS-STATE SETTING 430(5) APT MODELS 435(4) TESTING APT 436(3) SUMMARY 439(2) ARBITRAGE PRICING: CONTINUOUS-STATE, CONTINUOUS-TIME MODELS 441(30) THE ARBITRAGE PRINCIPLE IN CONTINUOUS TIME 441(4) TRADING STRATEGIES AND TRADING GAINS 443(2) ARBITRAGE PRICING IN CONTINUOUS-STATE, CONTINUOUS-TIME 445(2) OPTION PRICING 447(7) STOCK PRICE PROCESSES 447(1) HEDGING 448(1) THE BLACK-SCHOLES OPTION PRICING FORMULA 449(3) GENERALIZING THE PRICING OF EUROPEAN OPTIONS 452(2) STATE-PRICE DEFLATORS 454(3) EQUIVALENT MARTINGALE MEASURES 457(2) EQUIVALENT MARTINGALE MEASURES AND GIRSANOV'S THEOREM 459(4) THE DIFFUSION INVARIANCE PRINCIPLE 461(1) APPLICATION OF GIRSANOV'S THEOREM TO BLACK-SCHOLES OPTION PRICING FORMULA 462(1) EQUIVALENT MARTINGALE MEASURES AND COMPLETE MARKETS 463(1) EQUIVALENT MARTINGALE MEASURES AND STATE PRICES 464(2) ARBITRAGE PRICING WITH A PAYOFF RATE 466(1) IMPLICATIONS OF THE ABSENCE OF ARBITRAGE 467(1) WORKING WITH EQUIVALENT MARTINGALE MEASURES 468(1) SUMMARY 468(3) PORTFOLIO SELECTION USING MEAN-VARIANCE ANALYSIS 471(40) DIVERSIFICATION AS A CENTRAL THEME IN FINANCE 472(2) MARKOWITZ'S MEAN-VARIANCE ANALYSIS 474(3) CAPITAL MARKET LINE 477(5) DERIVING THE CAPITAL MARKET LINE 478(3) WHAT IS PORTFOLIO M? 481(1) RISK PREMIUM IN THE CML 482(1) ... 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