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Epps T. — Quantitative Finance: Its Development, Mathematical Foundations, and Current Scope
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Название: Quantitative Finance: Its Development, Mathematical Foundations, and Current Scope
Автор: Epps T.
Аннотация: A rigorous, yet accessible, introduction to essential topics in mathematical financePresented as a course on the topic, Quantitative Finance traces the evolution of financial theory and provides an overview of core topics associated with financial investments. With its thorough explanations and use of real-world examples, this book carefully outlines instructions and techniques for working with essential topics found within quantitative finance including portfolio theory, pricing of derivatives, decision theory, and the empirical behavior of prices.The author begins with introductory chapters on mathematical analysis and probability theory, which provide the needed tools for modeling portfolio choice and pricing in discrete time. Next, a review of the basic arithmetic of compounding as well as the relationships that exist among bond prices and spot and forward interest rates is presented.? Additional topics covered include:Dividend discount modelsMarkowitz mean-variance theoryThe Capital Asset Pricing ModelStatic?portfolio theory based on the expected-utility paradigmFamiliar probability models for marginal distributions of returns and the dynamic behavior of security pricesThe final chapters of the book delve into the paradigms of pricing and present the application of martingale pricing in advanced models of price dynamics. Also included is a step-by-step discussion on the use of Fourier methods to solve for arbitrage-free prices when underlying price dynamics are modeled in realistic, but complex ways.Throughout the book, the author presents insight on current approaches along with comments on the unique difficulties that exist in the study of financial markets. These reflections illustrate the evolving nature of the financial field and help readers develop analytical techniques and tools to apply in their everyday work. Exercises at the end of most chapters progress in difficulty, and selected worked-out solutions are available in the appendix. In addition, numerous empirical projects utilize MATLAB® and Minitab® to demonstrate the mathematical tools of finance for modeling the behavior of prices and markets. Data sets that accompany these projects can be found via the book's FTP site.Quantitative Finance is an excellent book for courses in quantitative finance or financial engineering at the upper-undergraduate and graduate levels. It is also a valuable resource for practitioners in related fields including engineering, finance, and economics.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2009
Количество страниц: 401
Добавлена в каталог: 16.08.2014
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Предметный указатель
Absolute continuity of functions 30
Absolute continuity of measures 24
Absolute risk aversion 108
Adapted process 171
Additively separable utility 198
Affine function 38 106
Allais' paradox 128
Almost everywhere 18
Almost sure/certain 26
apt see "Arbitrage pricing theory"
Arbitrage portfolio 249
Arbitrage pricing theory, criticisms of 251
Arbitrage pricing theory, description 248
Arbitrage, defined 247
Arbitrage, pricing by 9 59 247
ARCH/GARCH models 310
ARMA Models 310
Asynchronous trading effect 158
Autocorrelation function 156
Bates model see "SV-jump model"
Behavioral Finance 134
Bernoulli distribution 51
Beta coefficient 91
Bid-asked bounce 156
Bienayme — Galton — Watson process 324
Binomial distribution 51
Black — Scholes formulas 266 271
Black — Scholes formulas with time-varying volatility 349
Bonds, arbitrages among 252
Bonds, coupon 57 252
Bonds, default-free 58
Bonds, discount 57 252
Bonds, forward 63
Bonds, zero-coupon 57
Book-to-market anomaly 94 246
Borel sets 16
Borel — Cantelli lemma 44
Branching process model, description 324
Branching process model, option pricing under 343
Brownian motion, defined 167
Brownian motion, geometric 181 263
Brownian motion, properties of 167
Capital asset pricing model, multiperiod framework 219
Capital asset pricing model, single-period framework 87 245
Capital asset pricing model, tests of 92
CAPM see "Capital asset pricing model"
Cauchy distribution 51 148 345
Central limit theorems 45
Certainty effect 129
Certainty equivalent 108
CEV model see "Constant elasticity of variance"
Change-of-variable formula, multivariate 33
Change-of-variable formula, univariate 32
Characteristic function, applications in option pricing 339 351 354
Characteristic function, defined 336
Chi-squared distribution 151
Coefficient of variation 36
Common stock 6
Complete markets 302 326
Compound-events model 150 166
Compound-Poisson process 166
Conditional expectation, generally 38
Conditional expectation, process 267 351
Conditional expectation, tower property of 39 162 266
Conditional probability 26
Conditional variance 39
Constant elasticity of variance model 182 308
Contingent claims 3
Convergence in distribution 43
Convergence in probability 43
Convergence of sequences of functions 42
Convergence of sequences of numbers 42
Convergence, almost-sure 44
Convex function 37
Countable additivity 17
Countable set 15 29
Counting measure 17 26 30 31
Covariance matrix 38
Cox — Ingersoll — Ross model 301
Cumulant-generating function 46 153
Cumulative distribution function 29 32
Cumulative distribution function from characteristic function 339
Delta hedging 280
Delta of option 279
Derivative assets, defined 254
Descending factorial moments 41
Diffusion coefficient 181
Directing process 322
Discontinuous price processes 318
Dividend Discount Model 72 241
Dominated convergence 22 23 115
Drift term 181
Dynamic portfolio models 193 218
Dynamic pricing models 220 246 298
Dynamic programming 194
Early-exercise boundary 284
Efficiency of markets 139 160 229
Efficient portfolios 75
Ellsberg paradox 106
Equity premium 224
Equivalent measures see "Measure(s)"
Euler's formula 336
Event studies 230
Excess volatility 225 237
Exchange-traded funds 6
Expected value see "Mathematical expectation"
Expected-utility theory vs. mean-variance theory 117
Expected-utility theory, axioms 98
Expected-utility theory, criticisms of 127
Expected-utility theory, financial applications 103
Expected-utility theory, proof of theorem 101
Expected-utility theory, qualitative implications 109
Factor loading 80 248
Factor model 80 248
Fair-game property of martingales 162
Feynman — Kac solution 266 289
Field (of sets) 16
Filtration 171 267
Firm size anomaly 94 246
First-moment dependence 156 236
Fixed-income securities 6
Forward contract 63 255 269 296
Forward measure 302
Forward price 63 255
Forward rate 64
Fourier methods for pricing 339
Fourier transform 337 339
Fractals 170
Fubini's theorem 35
Fundamental PDE 264
Fundamental theorem of asset pricing 291
Futures contract 257 259
Gamma distribution 49 322
Gamma of option 279
Gamma process 322
Geometric Brownian motion 181 263
Girsanov's theorem 295 309 332
Growth optimality see "Optimal growth"
Habit persistence 225
Hansen — Jagannathan bound 224
Heston model 348
Heston model, compared with jump diffusion 320
Heston model, description 312
Heston model, option pricing under 350
Hobson — Rogers model 309
Idiosyncratic risk 80 248
Implicit volatility 279 282 286 314 318 334
Independence of events 27
Independence of random variables 33
Independence of sigma fields 33
Indicator function 12
Infinite divisibility 166
Informational efficiency 229
Integral, Ito 178
Integral, Lebesgue 20
Integral, Lebesgue — Stieltjes 20 31 34
Integral, Riemann 18 179
Integral, Riemann — Stieltjes 19
Integral, Stochastic 178 183
Integral, Stratonovich 190
Intensity parameter see "Poisson process"
Interest rate caps 7
Interest rate, compound 56
Interest rate, continuously compounded 56
Interest rate, forward 63
Interest rate, simple 55
Interest rate, spot 61
Inverse gaussian distribution 357
Ito process, defined 180
Ito process, quadratic variation of 182
Ito's formula for functions of a BM 185
Ito's formula, functions of jump diffusions 319 355
Ito's formula, functions of time and BM 186
Ito's formula, functions of time and Ito process 187
January effect 94 236
Jensen's inequality 37 107
Jump diffusion model, compared with Heston model 320
Jump diffusion model, description 318
Jump diffusion model, option pricing under 330 341
Kurtosis in stock returns 147
Kurtosis of normal distribution 47
Kurtosis, coefficient of 36
Lagrange multiplier 77
Law of total probability 27
Laws of large numbers 45 204
Lebesgue measure 17 26
Leverage effect 308
Lindeberg — Levy theorem 45
Lognormal distribution 48 143
Lucas model 220 236
Marginal distribution 32
Market portfolio 89
Markets for financial assets 4
Marking to market 257
Martingale measure, existence of 292
Martingale measure, uniqueness of 302 313 326
Martingale process in continuous time 171
Martingale process, conditional expectation as 267
Martingale process, defined 162
Martingale process, fair-game property 162 180
Martingale process, price as 162 223 292
Mathematical expectation, conditional 38
Mathematical expectation, generally 34
Mathematical expectation, properties of 36
Mean-reverting process 182 301 312
Mean-variance dominance 76
Mean-variance dominance in short holding periods 120
Mean-variance dominance, defined 117
Measurable function 20 28
Measurable space 25
Measure(s), -finite 17 23
Measure(s), absolutely continuous 24
Measure(s), changes of 23 41 290 295 299
Measure(s), equivalent 24 42 290
Measure(s), forward 302
Measure(s), generally 16
Measure(s), induced 28
Measure(s), monotone property of 17 26
Measure(s), natural 291
Mixture models 150 317 322
Moment-generating function 40 336
Moments see "Random variables"
Momentum in prices 240
Money-market fund 62
Monks, self-flagellating 106
Monotone convergence 22
Monotone sequence of sets 17
Multiplication rule 27
Mutual funds 6
Natural measure 291
Normal distribution 46 143
Normative models 71
Null sets/events 26 27 33 290
Numeraire 291 300 330
Numerical integration 340
Operational vs. calendar time 322
Optimal growth in continuous time 206
Optimal growth in discrete time 203
Optimal growth, basic concept 201
Options, American 283
Options, Black — Scholes formulas 266
Options, bounds on prices 275
Options, calls 262 297
Options, deltas of 279
Options, digital 297 303
Options, European 262 297
Options, gammas of 279
Options, properties of prices 277
Options, put-call parity 276
Options, puts 262 270 297
Options, threshold 298
Order notation 12
Partition 27
Point process 165
Poisson distribution 52 150
Poisson process 318
Poisson process, defined 165
Poisson process, intensity parameter of 165 318 357
Portfolio insurance 281
Positive models 71 127
Preference reversals 131
Preferred stock 6
Pricing function 222
Pricing kernel 221
Primary assets 6
Principle of optimality 195
Probability density function 30
Probability generating function 41 325 343
Probability limit 44 178
Probability mass function 30
Probability measure 25
Probability space 25
Prospect theory 129 226
Put-call parity 276 277
Quadratic covariation 189 352
Quadratic programming 77
Quadratic variation 170 179 182 352
Radon — Nikodym derivative 24 30 31
Radon — Nikodym theorem 24 42
Random variables, continuous 29
Random variables, defined 28
Random variables, discrete 29
Random variables, mixed 29
Random variables, moments of 36
Random variables, supports of 29
Random-walk hypothesis 160 235
Rate of return, continuously compounded 140
Rate of return, simple 73
Rational expectations 139 217 229
Reflection effect 130
Regime-switching models 357
Regression function 38
Relative risk aversion 108
Replication and uniqueness of martingale measure 303
Replication, dynamic 262
Replication, infeasibility in jump models 326
Replication, infeasibility in SV models 313
Replication, static 256 261
Risk aversion and diminishing marginal utility 133
Risk aversion, measures of 107
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