Essentials Of Stochastic Finance: Facts, Models, Theory Facts, Models, Theory

this Important Book Provides Information Necessary For Those Dealing With Stochastic Calculus And Pricing In The Models Of Financial Markets Operating Under Uncertainty; Introduces The Reader To The Main Concepts, Notions And Results Of Stochastic Financial Mathematics; And Develops Applications Of These Results To Various Kinds Of Calculations Required In Financial Engineering. It Also Answers The Requests Of Teachers Of Financial Mathematics And Engineering By Making A Bias Towards Probabilistic And Statistical Ideas And The Methods Of Stochastic Calculus In The Analysis Of Market Risks. Title ......Page 4 Contents ......Page 6 Foreword ......Page 14 Part 1 Facts, Models ......Page 18 1 Main Concepts, Structures, and Instruments ......Page 19 1. Financial Structures and Instruments ......Page 20 2. Financial Markets under Uncertainty. Classical Theories of the Dynamics of Financial Indexes, their Crtiics and Revision. Neoclassical Theories ......Page 52 3. Aims and Problems of Financial Theory, Engineering, and Actuarial Calculations ......Page 86 2 Stochastic Models. Discrete Time ......Page 97 1. Necessary Probabilistic Concepts and Several Models of the Dynamics of Market Prices ......Page 98 2. Linear Stochastic Models ......Page 134 3. Nonlinear Stochastic Conditionally Gaussian Models ......Page 169 4. Supplement: Dynamical Chaos Models ......Page 193 3 Stochastic Models. Continuous Time ......Page 205 1. Non-Gaussian Models of Distributions and Processes ......Page 206 2. Models with Self-Similarity. Fractality ......Page 238 3. Models Based on a Brownian Motion ......Page 253 4. Diffusion Models of the Evolution of Interest Rates, Stock and Bond Prices ......Page 295 5. Semimartingale Models ......Page 311 4 Statistical Analysis of Financial Data ......Page 331 1. Empirical Data. Probabilistic and Statistical Models of Their Description. Statistics of 'Ticks' ......Page 332 2. Statistics of One-Dimensional Distributions ......Page 344 3. Statistics of Volatility, Correlation Dependence, and Afereffect in Prices ......Page 362 4. Statistical Methods of R/S-Analysis ......Page 384 Part 2 Theory ......Page 398 5 Theory of Arbitrage in Stochastic Financial Models. Discrete Time ......Page 399 1. Investment Portfolio on a (B,S)-Market ......Page 400 2. Arbitrage-Free Market ......Page 427 3. Construction of Martingale Measure by Means of an Absolutely Continuous Change of Measure ......Page 450 4. Complete and Perfect Arbitrage-Free Markets ......Page 498 6 Theory of Pricing in Stochastic Financial Models. Discrete Time ......Page 519 1. European Hedge Pricing on Arbitrage-Free Markets ......Page 520 2. American Hedge Pricing on Arbitrage-Free Markets ......Page 542 3. Scheme of Series of 'Large' Arbitrage-Free Markets and Asymptotic Arbitrage ......Page 570 4. European Options on a Binomial (B,S)-Market ......Page 605 5. American Options on a Binomial (B,S)-Market ......Page 625 7 Theory of Arbitrage in Stochastic Financial Models. Continuous Time ......Page 649 1. Investment Portfolio in Semimartingale Models ......Page 650 2. Semimartingale Models without Opportunities for Arbitrage. Completeness ......Page 666 3. Semimartingale and Martingale Measures ......Page 679 4. Arbitrage, Completeness, and Hedge Pricing in Diffusion Models of Stock ......Page 721 5. Arbitrage, Completeness, and Hedge Pricing in Diffusion Models of Bonds ......Page 734 8 Theory of Pricing in Stochastic Financial Models. Continuous Time ......Page 751 1. European Options in Diffusion (B,S)-Stockmarkets......Page 752 2. American Options in Diffusion (B,S)-Stockmarkets. Case of an Infinite Time Horizon ......Page 768 3. American Options in Diffusion (B,S)-Stockmarkets. Finite Time Horizons ......Page 795 4. European and American Options in a Diffusion (B,P)-Bondmarket......Page 809 Bibliography ......Page 820 Index ......Page 842 Index of Symbols ......Page 850 Ch. I. Main concepts, structures, and instruments. Aims and problems of financial theory and financial engineering. 1. Financial structures and instruments. 2. Financial markets underuncertainty. Classical theories of the dynamics of financial indexes, their critics and revision. Neoclassical theories. 3. Aims and problems of financial theory, engineering, and actuarial calculations. [symbol] -- ch. II. Stochastic models. Discrete time. 1. Necessary probabilistic concept and several models of the dynamics of market prices. 2. Linear stochastic models. 3. Nonlinear stochastic conditionally Gaussian models. 4. Supplement: dynamical chaos models -- ch. III. Stochastic models. Continuous time. 1. Non-Gaussian models of distributions and processes. 2. Models with self-similarity. Fractality. 3. Models based on a Brownian motion. 4. Diffusion models of the evolution of interest rates, stock and bond prices. 5. Semimartingale models. ch. IV. Statistical analysis of financial data. 1. Empirical data. Probabilistic and statistical models of their description. Statistics of 'ticks'. 2. Statistics of one-dimensional distributions. 3. Statistics of volatility, correlation dependence, and aftereffect in prices. 4. Statistical R/S-analysis. ch. V. Theory of arbitrage in stochastic financial models. Discrete time. 1. Investment portfolio on a (B, S)-market. 2. Arbitrage-free market. 3. Construction of martingale measures by means of an absolutely continuous change of measure. 4. Complete and perfect arbitrage-free markets -- ch. VI . Theory of pricing in stochastic financial models. Discrete time. 1. European hedge pricing on arbitrage-free markets. 2. American hedge pricing on arbitrage-free markets. 3. Scheme of series of 'large' arbitrage-free markets and asymptotic arbitrage. 4. European options on a binomial (B, S)-market. 5. American options on a binomial (B, S)-market -- ch. VII. Theory of arbitrage in stochastic financial models. Continuous time. 1. Investment portfolio in semimartingale models. 2. Semimartingale models without opportunities for arbitrage. Completeness. 3. Semimartingale and martingale measures. 4. Arbitrage, completeness, and hedge pricing in diffusion models of stock. 5. Arbitrage, completeness, and hedge pricing in diffusion models of bonds -- ch. VIII. Theory of pricing in stochastic financial models. Continuous time. 1. European options in diffusion (B, S)-stockmarkets. 2. American options in diffusion (B, S)-stockmarkets. Case of an infinite time horizon. 3. American options in diffusion (B, S)-stockmarkets. Finite time horizons. 4. European and American options in a diffusion (B, P)-bondmarket This text provides information for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty. It introduces the reader to the main concepts, notions and results of stochastic financial mathematics, and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and stastical ideas and the methods of stochastic calculus in the analysis of market risks. In modern view (see, e.g., [79], [334], and [345]) financial theory and engineering must analyze the properties of financial structures and find most sensible ways to operate financial resources using various financial instruments and strategies with due account paid to such factors as time, risks, and (usually, random) environment.