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Quantitative finance : its development, mathematical foundations, and current scope / T.W. Epps.

By: Material type: TextTextPublisher: Hoboken, N.J. : Wiley, [2009]Copyright date: ©2009Description: xviii, 401 pages : illustrations ; 25 cmContent type:
  • text
Media type:
  • unmediated
Carrier type:
  • volume
ISBN:
  • 0470431997
  • 9780470431993
Subject(s): DDC classification:
  • 332.015195 22
LOC classification:
  • HG106 .E67 2009
Contents:
Part I. Perspective and Preparation -- 1. Introduction and Overview -- 1.1. An Elemental View of Assets and Markets -- 1.1.1. Assets as Bundles of Claims -- 1.1.2. Financial Markets as Transportation Agents -- 1.1.3. Why Is Transportation Desirable? -- 1.1.4. What Vehicles Are Available? -- 1.1.5. What Is There to Learn about Assets and Markets? -- 1.1.6. Why the Need for Quantitative Finance? -- 1.2. Where We Go from Here -- 2. Tools from Calculus and Analysis -- 2.1. Some Basics from Calculus -- 2.2. Elements of Measure Theory -- 2.2.1. Sets and Collections of Sets -- 2.2.2. Set Functions and Measures -- 2.3. Integration -- 2.3.1. Riemann-Stieltjes -- 2.3.2. Lebesgue /Lebesgue-Stieltjes -- 2.3.3. Properties of the Integral -- 2.4. Changes of Measure -- 3. Probability -- 3.1. Probability Spaces -- 3.2. Random Variables and Their Distributions -- 3.3. Independence of R.V.s -- 3.4. Expectation -- 3.4.1. Moments -- 3.4.2. Conditional Expectations and Moments -- 3.4.3. Generating Functions -- 3.5. Changes of Probability Measure -- 3.6. Convergence Concepts -- 3.7. Laws of Large Numbers and Central Limit Theorems -- 3.8. Important Models for Distributions -- 3.8.1. Continuous Models -- 3.8.2. Discrete Models -- Part II. Portfolios and Prices -- 4. Interest and Bond Prices -- 4.1. Interest Rates and Compounding -- 4.2. Bond Prices, Yields, and Spot Rates -- 4.3. Forward Bond Prices and Rates -- 4.4. Empirical Project #1 -- 5. Models of Portfolio Choice -- 5.1. Models That Ignore Risk -- 5.2. Mean-Variance Portfolio Theory -- 5.2.1. Mean-Variance 'Efficient' Portfolios -- 5.2.2. The Single-Index Model -- 5.3. Empirical Project #2 -- 6. Prices in a Mean-VarianceWorld -- 6.1. The Assumptions -- 6.2. The Derivation -- 6.3. Interpretation -- 6.4. Empirical Evidence -- 6.5. Some Reflections -- 7. Rational Decisions under Risk -- 7.1. The Setting and the Axioms -- 7.2. The Expected-Utility Theorem -- 7.3. Applying Expected-Utility Theory -- 7.3.1. Implementing EU Theory in Financial Modeling -- 7.3.2. Inferring Utilities and Beliefs -- 7.3.3. Qualitative Properties of Utility Functions -- 7.3.4. Measures of Risk Aversion -- 7.3.5. Examples of Utility Functions -- 7.3.6. Some Qualitative Implications of the EU Model -- 7.3.7. Stochastic Dominance -- 7.4. Is the Markowitz Investor Rational? -- 7.5. Empirical Project #3 -- 8. Observed Decisions under Risk -- 8.1. Evidence about Choices under Risk -- 8.1.1. Allais? Paradox -- 8.1.2. Prospect Theory -- 8.1.3. Preference Reversals -- 8.1.4. Risk Aversion and Diminishing Marginal Utility -- 8.2. Toward 'Behavioral' Finance -- 9. Distributions of Returns -- 9.1. Some Background -- 9.2. The Normal /Lognormal Model -- 9.3. The Stable Model -- 9.4. Mixture Models -- 9.5. Comparison and Evaluation -- 10. Dynamics of Prices and Returns -- 10.1. Evidence for First-Moment Independence -- 10.2. Random Walks and Martingales -- 10.3. Modeling Prices in Continuous Time -- 10.3.1. Poisson and Compound-Poisson Processes -- 10.3.2. Brownian Motions -- 10.3.3. Martingales in Continuous Time -- 10.4. Empirical Project #4 -- 11. Stochastic Calculus -- 11.1. Stochastic Integrals -- 11.1.1. Ito Integrals with Respect to a B.m -- 11.1.2. From It^o Integrals to It^o Processes -- 11.1.3. Quadratic-Variations of It^o Processes -- 11.1.4. Integrals with Respect to It^o Processes -- 11.2. Stochastic Differentials -- 11.3. Ito's Formula for Differentials -- 11.3.1. Functions of a B.m. Alone -- 11.3.2. Functions of Time and a B.m -- 11.3.3. Functions of Time and General It^o Processes -- 12. Portfolio Decisions over Time -- 12.1. The Consumption-Investment Problem -- 12.2. Dynamic Portfolio Decisions -- 12.2.1. Optimizing via Dynamic Programming -- 12.2.2. A Formulation with Additively-Separable Utility -- 13. Optimal Growth -- 13.1. Optimal Growth in Discrete Time -- 13.2. Optimal Growth in Continuous Time -- 13.3. Some Qualifications -- 13.4. Empirical Project #5 -- 14. Dynamic Models for Prices -- 14.1. Dynamic Optimization (Again) -- 14.2. Static Implications: The CAPM -- 14.3. Dynamic Implications: The Lucas Model -- 14.4. Assessment -- 14.4.1. The Puzzles -- 14.4.2. The Patches -- 14.4.3. Some Reflections -- 15. Efficient Markets -- 15.1. Event Studies -- 15.1.1. Methods -- 15.1.2. A Sample Study -- 15.2. Dynamic Tests -- 15.2.1. Early History -- 15.2.2. Implications of the Dynamic Models -- 15.2.3. Excess Volatility -- Part III. Paradigms for Pricing -- 16. Static Arbitrage Pricing -- 16.1. Pricing Paradigms: Optimization vs. Arbitrage -- 16.2. The APT -- 16.3. Arbitraging Bonds -- 16.4. Pricing a Simple Derivative Asset -- 17. Dynamic Arbitrage Pricing -- 17.1. Dynamic Replication -- 17.2. Modeling Prices of the Assets -- 17.3. The Fundamental P.D.E -- 17.3.1. The Feynman-Kac Solution to the P.D.E -- 17.3.2. Working out the Expectation -- 17.4. Allowing Dividends and Time-Varying Rates -- 18. Properties of Option Prices -- 18.1. Bounds on Prices of European Options -- 18.2. Properties of Black-Scholes Prices -- 18.3. Delta Hedging -- 18.4. Does Black-Scholes StillWork? -- 18.5. American-Style Options -- 18.6. Empirical Project #6 -- 19. Martingale Pricing -- 19.1. Some Preparation -- 19.2. Fundamental Theorem of Asset Pricing -- 19.3. Implications for Pricing Derivatives -- 19.4. Applications -- 19.5. Martingale vs. Equilibrium Pricing -- 19.6. Numeraires, Short Rates, and E.M.M.s -- 19.7. Replication & Uniqueness of the E.M.M -- 20. Modeling Volatility -- 20.1. Models with Price-Dependent Volatility -- 20.1.1. The C.E.V. Model -- 20.1.2. The Hobson-Rogers Model -- 20.2. ARCH /GARCH Models -- 20.3. Stochastic Volatility -- 20.4. Is Replication Possible? -- 21. Discontinuous Price Processes -- 21.1. Merton's Jump-Diffusion Model -- 21.2. The Variance-Gamma Model -- 21.3. Stock Prices as Branching Processes -- 21.4. Is Replication Possible? -- 22. Options on Jump Processes -- 22.1. Options under Jump-Diffusions -- 22.2. A Primer on Characteristic Functions -- 22.3. Using Fourier Methods to Price Options -- 22.4. Applications to Jump Models -- 23. Options on S.V. Processes -- 23.1. Independent Price /Volatility Shocks -- 23.2. Dependent Price /Volatility Shocks -- 23.3. Adding Jumps to the S.V. Model -- 23.4. Further Advances -- 23.5. Empirical Project #7.
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Book City Campus City Campus Main Collection 332.015195 EPP (Browse shelf(Opens below)) 1 Available A433371B

Includes bibliographical references (pages 391-395) and index.

Part I. Perspective and Preparation -- 1. Introduction and Overview -- 1.1. An Elemental View of Assets and Markets -- 1.1.1. Assets as Bundles of Claims -- 1.1.2. Financial Markets as Transportation Agents -- 1.1.3. Why Is Transportation Desirable? -- 1.1.4. What Vehicles Are Available? -- 1.1.5. What Is There to Learn about Assets and Markets? -- 1.1.6. Why the Need for Quantitative Finance? -- 1.2. Where We Go from Here -- 2. Tools from Calculus and Analysis -- 2.1. Some Basics from Calculus -- 2.2. Elements of Measure Theory -- 2.2.1. Sets and Collections of Sets -- 2.2.2. Set Functions and Measures -- 2.3. Integration -- 2.3.1. Riemann-Stieltjes -- 2.3.2. Lebesgue /Lebesgue-Stieltjes -- 2.3.3. Properties of the Integral -- 2.4. Changes of Measure -- 3. Probability -- 3.1. Probability Spaces -- 3.2. Random Variables and Their Distributions -- 3.3. Independence of R.V.s -- 3.4. Expectation -- 3.4.1. Moments -- 3.4.2. Conditional Expectations and Moments -- 3.4.3. Generating Functions -- 3.5. Changes of Probability Measure -- 3.6. Convergence Concepts -- 3.7. Laws of Large Numbers and Central Limit Theorems -- 3.8. Important Models for Distributions -- 3.8.1. Continuous Models -- 3.8.2. Discrete Models -- Part II. Portfolios and Prices -- 4. Interest and Bond Prices -- 4.1. Interest Rates and Compounding -- 4.2. Bond Prices, Yields, and Spot Rates -- 4.3. Forward Bond Prices and Rates -- 4.4. Empirical Project #1 -- 5. Models of Portfolio Choice -- 5.1. Models That Ignore Risk -- 5.2. Mean-Variance Portfolio Theory -- 5.2.1. Mean-Variance 'Efficient' Portfolios -- 5.2.2. The Single-Index Model -- 5.3. Empirical Project #2 -- 6. Prices in a Mean-VarianceWorld -- 6.1. The Assumptions -- 6.2. The Derivation -- 6.3. Interpretation -- 6.4. Empirical Evidence -- 6.5. Some Reflections -- 7. Rational Decisions under Risk -- 7.1. The Setting and the Axioms -- 7.2. The Expected-Utility Theorem -- 7.3. Applying Expected-Utility Theory -- 7.3.1. Implementing EU Theory in Financial Modeling -- 7.3.2. Inferring Utilities and Beliefs -- 7.3.3. Qualitative Properties of Utility Functions -- 7.3.4. Measures of Risk Aversion -- 7.3.5. Examples of Utility Functions -- 7.3.6. Some Qualitative Implications of the EU Model -- 7.3.7. Stochastic Dominance -- 7.4. Is the Markowitz Investor Rational? -- 7.5. Empirical Project #3 -- 8. Observed Decisions under Risk -- 8.1. Evidence about Choices under Risk -- 8.1.1. Allais? Paradox -- 8.1.2. Prospect Theory -- 8.1.3. Preference Reversals -- 8.1.4. Risk Aversion and Diminishing Marginal Utility -- 8.2. Toward 'Behavioral' Finance -- 9. Distributions of Returns -- 9.1. Some Background -- 9.2. The Normal /Lognormal Model -- 9.3. The Stable Model -- 9.4. Mixture Models -- 9.5. Comparison and Evaluation -- 10. Dynamics of Prices and Returns -- 10.1. Evidence for First-Moment Independence -- 10.2. Random Walks and Martingales -- 10.3. Modeling Prices in Continuous Time -- 10.3.1. Poisson and Compound-Poisson Processes -- 10.3.2. Brownian Motions -- 10.3.3. Martingales in Continuous Time -- 10.4. Empirical Project #4 -- 11. Stochastic Calculus -- 11.1. Stochastic Integrals -- 11.1.1. Ito Integrals with Respect to a B.m -- 11.1.2. From It^o Integrals to It^o Processes -- 11.1.3. Quadratic-Variations of It^o Processes -- 11.1.4. Integrals with Respect to It^o Processes -- 11.2. Stochastic Differentials -- 11.3. Ito's Formula for Differentials -- 11.3.1. Functions of a B.m. Alone -- 11.3.2. Functions of Time and a B.m -- 11.3.3. Functions of Time and General It^o Processes -- 12. Portfolio Decisions over Time -- 12.1. The Consumption-Investment Problem -- 12.2. Dynamic Portfolio Decisions -- 12.2.1. Optimizing via Dynamic Programming -- 12.2.2. A Formulation with Additively-Separable Utility -- 13. Optimal Growth -- 13.1. Optimal Growth in Discrete Time -- 13.2. Optimal Growth in Continuous Time -- 13.3. Some Qualifications -- 13.4. Empirical Project #5 -- 14. Dynamic Models for Prices -- 14.1. Dynamic Optimization (Again) -- 14.2. Static Implications: The CAPM -- 14.3. Dynamic Implications: The Lucas Model -- 14.4. Assessment -- 14.4.1. The Puzzles -- 14.4.2. The Patches -- 14.4.3. Some Reflections -- 15. Efficient Markets -- 15.1. Event Studies -- 15.1.1. Methods -- 15.1.2. A Sample Study -- 15.2. Dynamic Tests -- 15.2.1. Early History -- 15.2.2. Implications of the Dynamic Models -- 15.2.3. Excess Volatility -- Part III. Paradigms for Pricing -- 16. Static Arbitrage Pricing -- 16.1. Pricing Paradigms: Optimization vs. Arbitrage -- 16.2. The APT -- 16.3. Arbitraging Bonds -- 16.4. Pricing a Simple Derivative Asset -- 17. Dynamic Arbitrage Pricing -- 17.1. Dynamic Replication -- 17.2. Modeling Prices of the Assets -- 17.3. The Fundamental P.D.E -- 17.3.1. The Feynman-Kac Solution to the P.D.E -- 17.3.2. Working out the Expectation -- 17.4. Allowing Dividends and Time-Varying Rates -- 18. Properties of Option Prices -- 18.1. Bounds on Prices of European Options -- 18.2. Properties of Black-Scholes Prices -- 18.3. Delta Hedging -- 18.4. Does Black-Scholes StillWork? -- 18.5. American-Style Options -- 18.6. Empirical Project #6 -- 19. Martingale Pricing -- 19.1. Some Preparation -- 19.2. Fundamental Theorem of Asset Pricing -- 19.3. Implications for Pricing Derivatives -- 19.4. Applications -- 19.5. Martingale vs. Equilibrium Pricing -- 19.6. Numeraires, Short Rates, and E.M.M.s -- 19.7. Replication & Uniqueness of the E.M.M -- 20. Modeling Volatility -- 20.1. Models with Price-Dependent Volatility -- 20.1.1. The C.E.V. Model -- 20.1.2. The Hobson-Rogers Model -- 20.2. ARCH /GARCH Models -- 20.3. Stochastic Volatility -- 20.4. Is Replication Possible? -- 21. Discontinuous Price Processes -- 21.1. Merton's Jump-Diffusion Model -- 21.2. The Variance-Gamma Model -- 21.3. Stock Prices as Branching Processes -- 21.4. Is Replication Possible? -- 22. Options on Jump Processes -- 22.1. Options under Jump-Diffusions -- 22.2. A Primer on Characteristic Functions -- 22.3. Using Fourier Methods to Price Options -- 22.4. Applications to Jump Models -- 23. Options on S.V. Processes -- 23.1. Independent Price /Volatility Shocks -- 23.2. Dependent Price /Volatility Shocks -- 23.3. Adding Jumps to the S.V. Model -- 23.4. Further Advances -- 23.5. Empirical Project #7.

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