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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 ScopeАвтор: 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.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2009Количество страниц: 401Добавлена в каталог: 16.08.2014Операции: Положить на полку |
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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), 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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