Foundations of the Pricing of Financial Derivatives: Theory and Analysis
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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Newark
John Wiley & Sons, Incorporated
2024
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| Ausgabe: | 1st ed |
| Schriftenreihe: | Frank J. Fabozzi Series
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| Schlagworte: | |
| Online-Zugang: | DE-2070s |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 Online-Ressource (621 Seiten) |
| ISBN: | 9781394179671 |
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| 100 | 1 | |a Brooks, Robert E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Foundations of the Pricing of Financial Derivatives |b Theory and Analysis |
| 250 | |a 1st ed | ||
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| 505 | 8 | |a Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction and Overview -- 1.1 Motivation for This Book -- 1.2 What Is a Derivative? -- 1.3 Options Versus Forwards, Futures, and Swaps -- 1.4 Size and Scope of the Financial Derivatives Markets -- 1.5 Outline and Features of the Book -- 1.6 Final Thoughts and Preview -- Questions and Problems -- Notes -- Part I Basic Foundations for Derivative Pricing -- Chapter 2 Boundaries, Limits, and Conditions on Option Prices -- 2.1 Setup, Definitions, and Arbitrage -- 2.2 Absolute Minimum and Maximum Values -- 2.3 The Value of an American Option Relative to the Value of a European Option -- 2.4 The Value of an Option at Expiration -- 2.5 The Lower Bounds of European and American Options and the Optimality of Early Exercise -- 2.6 Differences in Option Values by Exercise Price -- 2.7 The Effect of Differences in Time to Expiration -- 2.8 The Convexity Rule -- 2.9 Put‐Call Parity -- 2.10 The Effect of Interest Rates on Option Prices -- 2.11 The Effect of Volatility on Option Prices -- 2.12 The Building Blocks of European Options -- 2.13 Recap and Preview -- Questions and Problems -- Notes -- Chapter 3 Elementary Review of Mathematics for Finance -- 3.1 Summation Notation -- 3.2 Product Notation -- 3.3 Logarithms and Exponentials -- 3.4 Series Formulas -- 3.5 Calculus Derivatives -- 3.6 Integration -- 3.7 Differential Equations -- 3.8 Recap and Preview -- Questions and Problems -- Notes -- Chapter 4 Elementary Review of Probability for Finance -- 4.1 Marginal, Conditional, and Joint Probabilities -- 4.2 Expectations, Variances, and Covariances of Discrete Random Variables -- 4.3 Continuous Random Variables -- 4.4 Some General Results in Probability Theory -- 4.5 Technical Introduction to Common Probability Distributions Used in Finance -- 4.6 Recap and Preview -- Questions and Problems | |
| 505 | 8 | |a Notes -- Chapter 5 Financial Applications of Probability Distributions -- 5.1 The Univariate Normal Probability Distribution -- 5.2 Contrasting the Normal with the Lognormal Probability Distribution -- 5.3 Bivariate Normal Probability Distribution -- 5.4 The Bivariate Lognormal Probability Distribution -- 5.5 Recap and Preview -- Appendix 5A An Excel Routine for the Bivariate Normal Probability -- Questions and Problems -- Notes -- Chapter 6 Basic Concepts in Valuing Risky Assets and Derivatives -- 6.1 Valuing Risky Assets -- 6.2 Risk‐Neutral Pricing in Discrete Time -- 6.3 Identical Assets and the Law of One Price -- 6.4 Derivative Contracts -- 6.5 A First Look at Valuing Options -- 6.6 A World of Risk‐Averse and Risk‐Neutral Investors -- 6.7 Pricing Options Under Risk Aversion -- 6.8 Recap and Preview -- Questions and Problems -- Notes -- Part II Discrete Time Derivatives Pricing Theory -- Chapter 7 The Binomial Model -- 7.1 The One‐Period Binomial Model for Calls -- 7.2 The One‐Period Binomial Model for Puts -- 7.3 Arbitraging Price Discrepancies -- 7.4 The Multiperiod Model -- 7.5 American Options and Early Exercise in the Binomial Framework -- 7.6 Dividends and Recombination -- 7.7 Path Independence and Path Dependence -- 7.8 Recap and Preview -- Appendix 7A Derivation of Equation (7.9) -- Appendix 7B Pascal's Triangle and the Binomial Model -- Questions and Problems -- Notes -- Chapter 8 Calculating the Greeks in the Binomial Model -- 8.1 Standard Approach -- 8.2 An Enhanced Method for Estimating Delta and Gamma -- 8.3 Numerical Examples -- 8.4 Dividends -- 8.5 Recap and Preview -- Questions and Problems -- Notes -- Chapter 9 Convergence of the Binomial Model to the Black‐Scholes‐Merton Model -- 9.1 Setting Up the Problem -- 9.2 The Hsia Proof -- 9.3 Put Options -- 9.4 Dividends -- 9.5 Recap and Preview -- Questions and Problems -- Notes | |
| 505 | 8 | |a Part III Continuous Time Derivatives Pricing Theory -- Chapter 10 The Basics of Brownian Motion and Wiener Processes -- 10.1 Brownian Motion -- 10.2 The Wiener Process -- 10.3 Properties of a Model of Asset Price Fluctuations -- 10.4 Building a Model of Asset Price Fluctuations -- 10.5 Simulating Brownian Motion and Wiener Processes -- 10.6 Formal Statement of Wiener Process Properties -- 10.7 Recap and Preview -- Appendix 10A Simulation of the Wiener Process and the Square of the Wiener Process for Successively Smaller Time Intervals -- Questions and Problems -- Notes -- Chapter 11 Stochastic Calculus and Itô's Lemma -- 11.1 A Result from Basic Calculus -- 11.2 Introducing Stochastic Calculus and Itô's Lemma -- 11.3 Itô's Integral -- 11.4 The Integral Form of Itô's Lemma -- 11.5 Some Additional Cases of Itô's Lemma -- 11.6 Recap and Preview -- Appendix 11A Technical Stochastic Integral Results -- 11A.1 Selected Stochastic Integral Results -- 11A.2 General Linear Theorem -- Questions and Problems -- Notes -- Chapter 12 Properties of the Lognormal and Normal Diffusion Processes for Modeling Assets -- 12.1 A Stochastic Process for the Asset Relative Return -- 12.2 A Stochastic Process for the Asset Price Change -- 12.3 Solving the Stochastic Differential Equation -- 12.4 Solutions to Stochastic Differential Equations Are Not Always the Same as Solutions to Corresponding Ordinary Differential Equations -- 12.5 Finding the Expected Future Asset Price -- 12.6 Geometric Brownian Motion or Arithmetic Brownian Motion? -- 12.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 13 Deriving the Black‐Scholes‐Merton Model -- 13.1 Derivation of the European Call Option Pricing Formula -- 13.2 The European Put Option Pricing Formula -- 13.3 Deriving the Black‐Scholes‐Merton Model as an Expected Value | |
| 505 | 8 | |a 13.4 Deriving the Black‐Scholes‐Merton Model as the Solution of a Partial Differential Equation -- 13.5 Decomposing the Black‐Scholes‐Merton Model into Binary Options -- 13.6 Black‐Scholes‐Merton Option Pricing When There Are Dividends -- 13.7 Selected Black‐Scholes‐Merton Model Limiting Results -- 13.8 Computing the Black‐Scholes‐Merton Option Pricing Model Values -- 13.9 Recap and Preview -- Appendix 13.A Deriving the Arithmetic Brownian Motion Option Pricing Model -- Questions and Problems -- Notes -- Chapter 14 The Greeks in the Black‐Scholes‐Merton Model -- 14.1 Delta: The First Derivative with Respect to the Underlying Price -- 14.2 Gamma: The Second Derivative with Respect to the Underlying Price -- 14.3 Theta: The First Derivative with Respect to Time -- 14.4 Verifying the Solution of the Partial Differential Equation -- 14.5 Selected Other Partial Derivatives of the Black‐Scholes‐Merton Model -- 14.6 Partial Derivatives of the Black‐Scholes‐Merton European Put Option Pricing Model -- 14.7 Incorporating Dividends -- 14.8 Greek Sensitivities -- 14.9 Elasticities -- 14.10 Extended Greeks of the Black‐Scholes‐Merton Option Pricing Model -- 14.11 Recap and Preview -- Questions and Problems -- Notes -- Chapter 15 Girsanov's Theorem in Option Pricing -- 15.1 The Martingale Representation Theorem -- 15.2 Introducing the Radon‐Nikodym Derivative by Changing the Drift for a Single Random Variable -- 15.3 A Complete Probability Space -- 15.4 Formal Statement of Girsanov's Theorem -- 15.5 Changing the Drift in a Continuous Time Stochastic Process -- 15.6 Changing the Drift of an Asset Price Process -- 15.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 16 Connecting Discrete and Continuous Brownian Motions -- 16.1 Brownian Motion in a Discrete World -- 16.2 Moving from a Discrete to a Continuous World | |
| 505 | 8 | |a 16.3 Changing the Probability Measure with the Radon‐Nikodym Derivative in Discrete Time -- 16.4 The Kolmogorov Equations -- 16.5 Recap and Preview -- Questions and Problems -- Notes -- Part IV Extensions and Generalizations of Derivative Pricing -- Chapter 17 Applying Linear Homogeneity to Option Pricing -- 17.1 Introduction to Exchange Options -- 17.2 Homogeneous Functions -- 17.3 Euler's Rule -- 17.4 Using Linear Homogeneity and Euler's Rule to Derive the Black‐Scholes‐Merton Model -- 17.5 Exchange Option Pricing -- 17.6 Spread Options3 -- 17.7 Forward Start Options -- 17.8 Recap and Preview -- Appendix 17A Linear Homogeneity and the Arithmetic Brownian Motion Model -- Appendix 17B Multivariate Itô's Lemma -- Appendix 17C Greeks of the Exchange Option Model -- Questions and Problems -- Notes -- Chapter 18 Compound Option Pricing -- 18.1 Equity as an Option -- 18.2 Valuing an Option on the Equity as a Compound Option -- 18.3 Compound Option Boundary Conditions and Parities -- 18.4 Geske's Approach to Valuing a Call on a Call -- 18.5 Characteristics of Geske's Call on Call Option -- 18.6 Geske's Call on Call Option Model and Linear Homogeneity -- 18.7 Generalized Compound Option Pricing Model -- 18.8 Installment Options -- 18.9 Recap and Preview -- Appendix 18A Selected Greeks of the Compound Option -- Questions and Problems -- Notes -- Chapter 19 American Call Option Pricing -- 19.1 Closed‐Form American Call Pricing: Roll‐Geske‐Whaley -- 19.2 The Two‐Payment Case -- 19.3 Recap and Preview -- Appendix 19A Numerical Example of the One‐Dividend Model -- Questions and Problems -- Notes -- Chapter 20 American Put Option Pricing -- 20.1 The Nature of the Problem of Pricing an American Put -- 20.2 The American Put as a Series of Compound Options -- 20.3 Recap and Preview -- Questions and Problems -- Notes -- Chapter 21 Min‐Max Option Pricing | |
| 505 | 8 | |a 21.1 Characteristics of Stulz's Min‐Max Option | |
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Datensatz im Suchindex
| _version_ | 1814902774162259968 |
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| adam_text | |
| any_adam_object | |
| author | Brooks, Robert E. |
| author_facet | Brooks, Robert E. |
| author_role | aut |
| author_sort | Brooks, Robert E. |
| author_variant | r e b re reb |
| building | Verbundindex |
| bvnumber | BV049871689 |
| classification_rvk | QK 660 QK 800 |
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| contents | Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction and Overview -- 1.1 Motivation for This Book -- 1.2 What Is a Derivative? -- 1.3 Options Versus Forwards, Futures, and Swaps -- 1.4 Size and Scope of the Financial Derivatives Markets -- 1.5 Outline and Features of the Book -- 1.6 Final Thoughts and Preview -- Questions and Problems -- Notes -- Part I Basic Foundations for Derivative Pricing -- Chapter 2 Boundaries, Limits, and Conditions on Option Prices -- 2.1 Setup, Definitions, and Arbitrage -- 2.2 Absolute Minimum and Maximum Values -- 2.3 The Value of an American Option Relative to the Value of a European Option -- 2.4 The Value of an Option at Expiration -- 2.5 The Lower Bounds of European and American Options and the Optimality of Early Exercise -- 2.6 Differences in Option Values by Exercise Price -- 2.7 The Effect of Differences in Time to Expiration -- 2.8 The Convexity Rule -- 2.9 Put‐Call Parity -- 2.10 The Effect of Interest Rates on Option Prices -- 2.11 The Effect of Volatility on Option Prices -- 2.12 The Building Blocks of European Options -- 2.13 Recap and Preview -- Questions and Problems -- Notes -- Chapter 3 Elementary Review of Mathematics for Finance -- 3.1 Summation Notation -- 3.2 Product Notation -- 3.3 Logarithms and Exponentials -- 3.4 Series Formulas -- 3.5 Calculus Derivatives -- 3.6 Integration -- 3.7 Differential Equations -- 3.8 Recap and Preview -- Questions and Problems -- Notes -- Chapter 4 Elementary Review of Probability for Finance -- 4.1 Marginal, Conditional, and Joint Probabilities -- 4.2 Expectations, Variances, and Covariances of Discrete Random Variables -- 4.3 Continuous Random Variables -- 4.4 Some General Results in Probability Theory -- 4.5 Technical Introduction to Common Probability Distributions Used in Finance -- 4.6 Recap and Preview -- Questions and Problems Notes -- Chapter 5 Financial Applications of Probability Distributions -- 5.1 The Univariate Normal Probability Distribution -- 5.2 Contrasting the Normal with the Lognormal Probability Distribution -- 5.3 Bivariate Normal Probability Distribution -- 5.4 The Bivariate Lognormal Probability Distribution -- 5.5 Recap and Preview -- Appendix 5A An Excel Routine for the Bivariate Normal Probability -- Questions and Problems -- Notes -- Chapter 6 Basic Concepts in Valuing Risky Assets and Derivatives -- 6.1 Valuing Risky Assets -- 6.2 Risk‐Neutral Pricing in Discrete Time -- 6.3 Identical Assets and the Law of One Price -- 6.4 Derivative Contracts -- 6.5 A First Look at Valuing Options -- 6.6 A World of Risk‐Averse and Risk‐Neutral Investors -- 6.7 Pricing Options Under Risk Aversion -- 6.8 Recap and Preview -- Questions and Problems -- Notes -- Part II Discrete Time Derivatives Pricing Theory -- Chapter 7 The Binomial Model -- 7.1 The One‐Period Binomial Model for Calls -- 7.2 The One‐Period Binomial Model for Puts -- 7.3 Arbitraging Price Discrepancies -- 7.4 The Multiperiod Model -- 7.5 American Options and Early Exercise in the Binomial Framework -- 7.6 Dividends and Recombination -- 7.7 Path Independence and Path Dependence -- 7.8 Recap and Preview -- Appendix 7A Derivation of Equation (7.9) -- Appendix 7B Pascal's Triangle and the Binomial Model -- Questions and Problems -- Notes -- Chapter 8 Calculating the Greeks in the Binomial Model -- 8.1 Standard Approach -- 8.2 An Enhanced Method for Estimating Delta and Gamma -- 8.3 Numerical Examples -- 8.4 Dividends -- 8.5 Recap and Preview -- Questions and Problems -- Notes -- Chapter 9 Convergence of the Binomial Model to the Black‐Scholes‐Merton Model -- 9.1 Setting Up the Problem -- 9.2 The Hsia Proof -- 9.3 Put Options -- 9.4 Dividends -- 9.5 Recap and Preview -- Questions and Problems -- Notes Part III Continuous Time Derivatives Pricing Theory -- Chapter 10 The Basics of Brownian Motion and Wiener Processes -- 10.1 Brownian Motion -- 10.2 The Wiener Process -- 10.3 Properties of a Model of Asset Price Fluctuations -- 10.4 Building a Model of Asset Price Fluctuations -- 10.5 Simulating Brownian Motion and Wiener Processes -- 10.6 Formal Statement of Wiener Process Properties -- 10.7 Recap and Preview -- Appendix 10A Simulation of the Wiener Process and the Square of the Wiener Process for Successively Smaller Time Intervals -- Questions and Problems -- Notes -- Chapter 11 Stochastic Calculus and Itô's Lemma -- 11.1 A Result from Basic Calculus -- 11.2 Introducing Stochastic Calculus and Itô's Lemma -- 11.3 Itô's Integral -- 11.4 The Integral Form of Itô's Lemma -- 11.5 Some Additional Cases of Itô's Lemma -- 11.6 Recap and Preview -- Appendix 11A Technical Stochastic Integral Results -- 11A.1 Selected Stochastic Integral Results -- 11A.2 General Linear Theorem -- Questions and Problems -- Notes -- Chapter 12 Properties of the Lognormal and Normal Diffusion Processes for Modeling Assets -- 12.1 A Stochastic Process for the Asset Relative Return -- 12.2 A Stochastic Process for the Asset Price Change -- 12.3 Solving the Stochastic Differential Equation -- 12.4 Solutions to Stochastic Differential Equations Are Not Always the Same as Solutions to Corresponding Ordinary Differential Equations -- 12.5 Finding the Expected Future Asset Price -- 12.6 Geometric Brownian Motion or Arithmetic Brownian Motion? -- 12.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 13 Deriving the Black‐Scholes‐Merton Model -- 13.1 Derivation of the European Call Option Pricing Formula -- 13.2 The European Put Option Pricing Formula -- 13.3 Deriving the Black‐Scholes‐Merton Model as an Expected Value 13.4 Deriving the Black‐Scholes‐Merton Model as the Solution of a Partial Differential Equation -- 13.5 Decomposing the Black‐Scholes‐Merton Model into Binary Options -- 13.6 Black‐Scholes‐Merton Option Pricing When There Are Dividends -- 13.7 Selected Black‐Scholes‐Merton Model Limiting Results -- 13.8 Computing the Black‐Scholes‐Merton Option Pricing Model Values -- 13.9 Recap and Preview -- Appendix 13.A Deriving the Arithmetic Brownian Motion Option Pricing Model -- Questions and Problems -- Notes -- Chapter 14 The Greeks in the Black‐Scholes‐Merton Model -- 14.1 Delta: The First Derivative with Respect to the Underlying Price -- 14.2 Gamma: The Second Derivative with Respect to the Underlying Price -- 14.3 Theta: The First Derivative with Respect to Time -- 14.4 Verifying the Solution of the Partial Differential Equation -- 14.5 Selected Other Partial Derivatives of the Black‐Scholes‐Merton Model -- 14.6 Partial Derivatives of the Black‐Scholes‐Merton European Put Option Pricing Model -- 14.7 Incorporating Dividends -- 14.8 Greek Sensitivities -- 14.9 Elasticities -- 14.10 Extended Greeks of the Black‐Scholes‐Merton Option Pricing Model -- 14.11 Recap and Preview -- Questions and Problems -- Notes -- Chapter 15 Girsanov's Theorem in Option Pricing -- 15.1 The Martingale Representation Theorem -- 15.2 Introducing the Radon‐Nikodym Derivative by Changing the Drift for a Single Random Variable -- 15.3 A Complete Probability Space -- 15.4 Formal Statement of Girsanov's Theorem -- 15.5 Changing the Drift in a Continuous Time Stochastic Process -- 15.6 Changing the Drift of an Asset Price Process -- 15.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 16 Connecting Discrete and Continuous Brownian Motions -- 16.1 Brownian Motion in a Discrete World -- 16.2 Moving from a Discrete to a Continuous World 16.3 Changing the Probability Measure with the Radon‐Nikodym Derivative in Discrete Time -- 16.4 The Kolmogorov Equations -- 16.5 Recap and Preview -- Questions and Problems -- Notes -- Part IV Extensions and Generalizations of Derivative Pricing -- Chapter 17 Applying Linear Homogeneity to Option Pricing -- 17.1 Introduction to Exchange Options -- 17.2 Homogeneous Functions -- 17.3 Euler's Rule -- 17.4 Using Linear Homogeneity and Euler's Rule to Derive the Black‐Scholes‐Merton Model -- 17.5 Exchange Option Pricing -- 17.6 Spread Options3 -- 17.7 Forward Start Options -- 17.8 Recap and Preview -- Appendix 17A Linear Homogeneity and the Arithmetic Brownian Motion Model -- Appendix 17B Multivariate Itô's Lemma -- Appendix 17C Greeks of the Exchange Option Model -- Questions and Problems -- Notes -- Chapter 18 Compound Option Pricing -- 18.1 Equity as an Option -- 18.2 Valuing an Option on the Equity as a Compound Option -- 18.3 Compound Option Boundary Conditions and Parities -- 18.4 Geske's Approach to Valuing a Call on a Call -- 18.5 Characteristics of Geske's Call on Call Option -- 18.6 Geske's Call on Call Option Model and Linear Homogeneity -- 18.7 Generalized Compound Option Pricing Model -- 18.8 Installment Options -- 18.9 Recap and Preview -- Appendix 18A Selected Greeks of the Compound Option -- Questions and Problems -- Notes -- Chapter 19 American Call Option Pricing -- 19.1 Closed‐Form American Call Pricing: Roll‐Geske‐Whaley -- 19.2 The Two‐Payment Case -- 19.3 Recap and Preview -- Appendix 19A Numerical Example of the One‐Dividend Model -- Questions and Problems -- Notes -- Chapter 20 American Put Option Pricing -- 20.1 The Nature of the Problem of Pricing an American Put -- 20.2 The American Put as a Series of Compound Options -- 20.3 Recap and Preview -- Questions and Problems -- Notes -- Chapter 21 Min‐Max Option Pricing 21.1 Characteristics of Stulz's Min‐Max Option |
| ctrlnum | (ZDB-30-PQE)EBC31093693 (ZDB-30-PAD)EBC31093693 (ZDB-89-EBL)EBL31093693 (OCoLC)1419872061 (DE-599)BVBBV049871689 |
| dewey-full | 332.6457 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.6457 |
| dewey-search | 332.6457 |
| dewey-sort | 3332.6457 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | 1st ed |
| format | Electronic eBook |
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Fabozzi Series</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Description based on publisher supplied metadata and other sources</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction and Overview -- 1.1 Motivation for This Book -- 1.2 What Is a Derivative? -- 1.3 Options Versus Forwards, Futures, and Swaps -- 1.4 Size and Scope of the Financial Derivatives Markets -- 1.5 Outline and Features of the Book -- 1.6 Final Thoughts and Preview -- Questions and Problems -- Notes -- Part I Basic Foundations for Derivative Pricing -- Chapter 2 Boundaries, Limits, and Conditions on Option Prices -- 2.1 Setup, Definitions, and Arbitrage -- 2.2 Absolute Minimum and Maximum Values -- 2.3 The Value of an American Option Relative to the Value of a European Option -- 2.4 The Value of an Option at Expiration -- 2.5 The Lower Bounds of European and American Options and the Optimality of Early Exercise -- 2.6 Differences in Option Values by Exercise Price -- 2.7 The Effect of Differences in Time to Expiration -- 2.8 The Convexity Rule -- 2.9 Put‐Call Parity -- 2.10 The Effect of Interest Rates on Option Prices -- 2.11 The Effect of Volatility on Option Prices -- 2.12 The Building Blocks of European Options -- 2.13 Recap and Preview -- Questions and Problems -- Notes -- Chapter 3 Elementary Review of Mathematics for Finance -- 3.1 Summation Notation -- 3.2 Product Notation -- 3.3 Logarithms and Exponentials -- 3.4 Series Formulas -- 3.5 Calculus Derivatives -- 3.6 Integration -- 3.7 Differential Equations -- 3.8 Recap and Preview -- Questions and Problems -- Notes -- Chapter 4 Elementary Review of Probability for Finance -- 4.1 Marginal, Conditional, and Joint Probabilities -- 4.2 Expectations, Variances, and Covariances of Discrete Random Variables -- 4.3 Continuous Random Variables -- 4.4 Some General Results in Probability Theory -- 4.5 Technical Introduction to Common Probability Distributions Used in Finance -- 4.6 Recap and Preview -- Questions and Problems</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Notes -- Chapter 5 Financial Applications of Probability Distributions -- 5.1 The Univariate Normal Probability Distribution -- 5.2 Contrasting the Normal with the Lognormal Probability Distribution -- 5.3 Bivariate Normal Probability Distribution -- 5.4 The Bivariate Lognormal Probability Distribution -- 5.5 Recap and Preview -- Appendix 5A An Excel Routine for the Bivariate Normal Probability -- Questions and Problems -- Notes -- Chapter 6 Basic Concepts in Valuing Risky Assets and Derivatives -- 6.1 Valuing Risky Assets -- 6.2 Risk‐Neutral Pricing in Discrete Time -- 6.3 Identical Assets and the Law of One Price -- 6.4 Derivative Contracts -- 6.5 A First Look at Valuing Options -- 6.6 A World of Risk‐Averse and Risk‐Neutral Investors -- 6.7 Pricing Options Under Risk Aversion -- 6.8 Recap and Preview -- Questions and Problems -- Notes -- Part II Discrete Time Derivatives Pricing Theory -- Chapter 7 The Binomial Model -- 7.1 The One‐Period Binomial Model for Calls -- 7.2 The One‐Period Binomial Model for Puts -- 7.3 Arbitraging Price Discrepancies -- 7.4 The Multiperiod Model -- 7.5 American Options and Early Exercise in the Binomial Framework -- 7.6 Dividends and Recombination -- 7.7 Path Independence and Path Dependence -- 7.8 Recap and Preview -- Appendix 7A Derivation of Equation (7.9) -- Appendix 7B Pascal's Triangle and the Binomial Model -- Questions and Problems -- Notes -- Chapter 8 Calculating the Greeks in the Binomial Model -- 8.1 Standard Approach -- 8.2 An Enhanced Method for Estimating Delta and Gamma -- 8.3 Numerical Examples -- 8.4 Dividends -- 8.5 Recap and Preview -- Questions and Problems -- Notes -- Chapter 9 Convergence of the Binomial Model to the Black‐Scholes‐Merton Model -- 9.1 Setting Up the Problem -- 9.2 The Hsia Proof -- 9.3 Put Options -- 9.4 Dividends -- 9.5 Recap and Preview -- Questions and Problems -- Notes</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Part III Continuous Time Derivatives Pricing Theory -- Chapter 10 The Basics of Brownian Motion and Wiener Processes -- 10.1 Brownian Motion -- 10.2 The Wiener Process -- 10.3 Properties of a Model of Asset Price Fluctuations -- 10.4 Building a Model of Asset Price Fluctuations -- 10.5 Simulating Brownian Motion and Wiener Processes -- 10.6 Formal Statement of Wiener Process Properties -- 10.7 Recap and Preview -- Appendix 10A Simulation of the Wiener Process and the Square of the Wiener Process for Successively Smaller Time Intervals -- Questions and Problems -- Notes -- Chapter 11 Stochastic Calculus and Itô's Lemma -- 11.1 A Result from Basic Calculus -- 11.2 Introducing Stochastic Calculus and Itô's Lemma -- 11.3 Itô's Integral -- 11.4 The Integral Form of Itô's Lemma -- 11.5 Some Additional Cases of Itô's Lemma -- 11.6 Recap and Preview -- Appendix 11A Technical Stochastic Integral Results -- 11A.1 Selected Stochastic Integral Results -- 11A.2 General Linear Theorem -- Questions and Problems -- Notes -- Chapter 12 Properties of the Lognormal and Normal Diffusion Processes for Modeling Assets -- 12.1 A Stochastic Process for the Asset Relative Return -- 12.2 A Stochastic Process for the Asset Price Change -- 12.3 Solving the Stochastic Differential Equation -- 12.4 Solutions to Stochastic Differential Equations Are Not Always the Same as Solutions to Corresponding Ordinary Differential Equations -- 12.5 Finding the Expected Future Asset Price -- 12.6 Geometric Brownian Motion or Arithmetic Brownian Motion? -- 12.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 13 Deriving the Black‐Scholes‐Merton Model -- 13.1 Derivation of the European Call Option Pricing Formula -- 13.2 The European Put Option Pricing Formula -- 13.3 Deriving the Black‐Scholes‐Merton Model as an Expected Value</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">13.4 Deriving the Black‐Scholes‐Merton Model as the Solution of a Partial Differential Equation -- 13.5 Decomposing the Black‐Scholes‐Merton Model into Binary Options -- 13.6 Black‐Scholes‐Merton Option Pricing When There Are Dividends -- 13.7 Selected Black‐Scholes‐Merton Model Limiting Results -- 13.8 Computing the Black‐Scholes‐Merton Option Pricing Model Values -- 13.9 Recap and Preview -- Appendix 13.A Deriving the Arithmetic Brownian Motion Option Pricing Model -- Questions and Problems -- Notes -- Chapter 14 The Greeks in the Black‐Scholes‐Merton Model -- 14.1 Delta: The First Derivative with Respect to the Underlying Price -- 14.2 Gamma: The Second Derivative with Respect to the Underlying Price -- 14.3 Theta: The First Derivative with Respect to Time -- 14.4 Verifying the Solution of the Partial Differential Equation -- 14.5 Selected Other Partial Derivatives of the Black‐Scholes‐Merton Model -- 14.6 Partial Derivatives of the Black‐Scholes‐Merton European Put Option Pricing Model -- 14.7 Incorporating Dividends -- 14.8 Greek Sensitivities -- 14.9 Elasticities -- 14.10 Extended Greeks of the Black‐Scholes‐Merton Option Pricing Model -- 14.11 Recap and Preview -- Questions and Problems -- Notes -- Chapter 15 Girsanov's Theorem in Option Pricing -- 15.1 The Martingale Representation Theorem -- 15.2 Introducing the Radon‐Nikodym Derivative by Changing the Drift for a Single Random Variable -- 15.3 A Complete Probability Space -- 15.4 Formal Statement of Girsanov's Theorem -- 15.5 Changing the Drift in a Continuous Time Stochastic Process -- 15.6 Changing the Drift of an Asset Price Process -- 15.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 16 Connecting Discrete and Continuous Brownian Motions -- 16.1 Brownian Motion in a Discrete World -- 16.2 Moving from a Discrete to a Continuous World</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">16.3 Changing the Probability Measure with the Radon‐Nikodym Derivative in Discrete Time -- 16.4 The Kolmogorov Equations -- 16.5 Recap and Preview -- Questions and Problems -- Notes -- Part IV Extensions and Generalizations of Derivative Pricing -- Chapter 17 Applying Linear Homogeneity to Option Pricing -- 17.1 Introduction to Exchange Options -- 17.2 Homogeneous Functions -- 17.3 Euler's Rule -- 17.4 Using Linear Homogeneity and Euler's Rule to Derive the Black‐Scholes‐Merton Model -- 17.5 Exchange Option Pricing -- 17.6 Spread Options3 -- 17.7 Forward Start Options -- 17.8 Recap and Preview -- Appendix 17A Linear Homogeneity and the Arithmetic Brownian Motion Model -- Appendix 17B Multivariate Itô's Lemma -- Appendix 17C Greeks of the Exchange Option Model -- Questions and Problems -- Notes -- Chapter 18 Compound Option Pricing -- 18.1 Equity as an Option -- 18.2 Valuing an Option on the Equity as a Compound Option -- 18.3 Compound Option Boundary Conditions and Parities -- 18.4 Geske's Approach to Valuing a Call on a Call -- 18.5 Characteristics of Geske's Call on Call Option -- 18.6 Geske's Call on Call Option Model and Linear Homogeneity -- 18.7 Generalized Compound Option Pricing Model -- 18.8 Installment Options -- 18.9 Recap and Preview -- Appendix 18A Selected Greeks of the Compound Option -- Questions and Problems -- Notes -- Chapter 19 American Call Option Pricing -- 19.1 Closed‐Form American Call Pricing: Roll‐Geske‐Whaley -- 19.2 The Two‐Payment Case -- 19.3 Recap and Preview -- Appendix 19A Numerical Example of the One‐Dividend Model -- Questions and Problems -- Notes -- Chapter 20 American Put Option Pricing -- 20.1 The Nature of the Problem of Pricing an American Put -- 20.2 The American Put as a Series of Compound Options -- 20.3 Recap and Preview -- Questions and Problems -- Notes -- Chapter 21 Min‐Max Option Pricing</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">21.1 Characteristics of 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| id | DE-604.BV049871689 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-05T17:02:42Z |
| institution | BVB |
| isbn | 9781394179671 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035211164 |
| oclc_num | 1419872061 |
| open_access_boolean | |
| owner | DE-2070s |
| owner_facet | DE-2070s |
| physical | 1 Online-Ressource (621 Seiten) |
| psigel | ZDB-30-PQE ZDB-30-PQE HWR_PDA_PQE |
| publishDate | 2024 |
| publishDateSearch | 2024 |
| publishDateSort | 2024 |
| publisher | John Wiley & Sons, Incorporated |
| record_format | marc |
| series2 | Frank J. Fabozzi Series |
| spelling | Brooks, Robert E. Verfasser aut Foundations of the Pricing of Financial Derivatives Theory and Analysis 1st ed Newark John Wiley & Sons, Incorporated 2024 ©2024 1 Online-Ressource (621 Seiten) txt rdacontent c rdamedia cr rdacarrier Frank J. Fabozzi Series Description based on publisher supplied metadata and other sources Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction and Overview -- 1.1 Motivation for This Book -- 1.2 What Is a Derivative? -- 1.3 Options Versus Forwards, Futures, and Swaps -- 1.4 Size and Scope of the Financial Derivatives Markets -- 1.5 Outline and Features of the Book -- 1.6 Final Thoughts and Preview -- Questions and Problems -- Notes -- Part I Basic Foundations for Derivative Pricing -- Chapter 2 Boundaries, Limits, and Conditions on Option Prices -- 2.1 Setup, Definitions, and Arbitrage -- 2.2 Absolute Minimum and Maximum Values -- 2.3 The Value of an American Option Relative to the Value of a European Option -- 2.4 The Value of an Option at Expiration -- 2.5 The Lower Bounds of European and American Options and the Optimality of Early Exercise -- 2.6 Differences in Option Values by Exercise Price -- 2.7 The Effect of Differences in Time to Expiration -- 2.8 The Convexity Rule -- 2.9 Put‐Call Parity -- 2.10 The Effect of Interest Rates on Option Prices -- 2.11 The Effect of Volatility on Option Prices -- 2.12 The Building Blocks of European Options -- 2.13 Recap and Preview -- Questions and Problems -- Notes -- Chapter 3 Elementary Review of Mathematics for Finance -- 3.1 Summation Notation -- 3.2 Product Notation -- 3.3 Logarithms and Exponentials -- 3.4 Series Formulas -- 3.5 Calculus Derivatives -- 3.6 Integration -- 3.7 Differential Equations -- 3.8 Recap and Preview -- Questions and Problems -- Notes -- Chapter 4 Elementary Review of Probability for Finance -- 4.1 Marginal, Conditional, and Joint Probabilities -- 4.2 Expectations, Variances, and Covariances of Discrete Random Variables -- 4.3 Continuous Random Variables -- 4.4 Some General Results in Probability Theory -- 4.5 Technical Introduction to Common Probability Distributions Used in Finance -- 4.6 Recap and Preview -- Questions and Problems Notes -- Chapter 5 Financial Applications of Probability Distributions -- 5.1 The Univariate Normal Probability Distribution -- 5.2 Contrasting the Normal with the Lognormal Probability Distribution -- 5.3 Bivariate Normal Probability Distribution -- 5.4 The Bivariate Lognormal Probability Distribution -- 5.5 Recap and Preview -- Appendix 5A An Excel Routine for the Bivariate Normal Probability -- Questions and Problems -- Notes -- Chapter 6 Basic Concepts in Valuing Risky Assets and Derivatives -- 6.1 Valuing Risky Assets -- 6.2 Risk‐Neutral Pricing in Discrete Time -- 6.3 Identical Assets and the Law of One Price -- 6.4 Derivative Contracts -- 6.5 A First Look at Valuing Options -- 6.6 A World of Risk‐Averse and Risk‐Neutral Investors -- 6.7 Pricing Options Under Risk Aversion -- 6.8 Recap and Preview -- Questions and Problems -- Notes -- Part II Discrete Time Derivatives Pricing Theory -- Chapter 7 The Binomial Model -- 7.1 The One‐Period Binomial Model for Calls -- 7.2 The One‐Period Binomial Model for Puts -- 7.3 Arbitraging Price Discrepancies -- 7.4 The Multiperiod Model -- 7.5 American Options and Early Exercise in the Binomial Framework -- 7.6 Dividends and Recombination -- 7.7 Path Independence and Path Dependence -- 7.8 Recap and Preview -- Appendix 7A Derivation of Equation (7.9) -- Appendix 7B Pascal's Triangle and the Binomial Model -- Questions and Problems -- Notes -- Chapter 8 Calculating the Greeks in the Binomial Model -- 8.1 Standard Approach -- 8.2 An Enhanced Method for Estimating Delta and Gamma -- 8.3 Numerical Examples -- 8.4 Dividends -- 8.5 Recap and Preview -- Questions and Problems -- Notes -- Chapter 9 Convergence of the Binomial Model to the Black‐Scholes‐Merton Model -- 9.1 Setting Up the Problem -- 9.2 The Hsia Proof -- 9.3 Put Options -- 9.4 Dividends -- 9.5 Recap and Preview -- Questions and Problems -- Notes Part III Continuous Time Derivatives Pricing Theory -- Chapter 10 The Basics of Brownian Motion and Wiener Processes -- 10.1 Brownian Motion -- 10.2 The Wiener Process -- 10.3 Properties of a Model of Asset Price Fluctuations -- 10.4 Building a Model of Asset Price Fluctuations -- 10.5 Simulating Brownian Motion and Wiener Processes -- 10.6 Formal Statement of Wiener Process Properties -- 10.7 Recap and Preview -- Appendix 10A Simulation of the Wiener Process and the Square of the Wiener Process for Successively Smaller Time Intervals -- Questions and Problems -- Notes -- Chapter 11 Stochastic Calculus and Itô's Lemma -- 11.1 A Result from Basic Calculus -- 11.2 Introducing Stochastic Calculus and Itô's Lemma -- 11.3 Itô's Integral -- 11.4 The Integral Form of Itô's Lemma -- 11.5 Some Additional Cases of Itô's Lemma -- 11.6 Recap and Preview -- Appendix 11A Technical Stochastic Integral Results -- 11A.1 Selected Stochastic Integral Results -- 11A.2 General Linear Theorem -- Questions and Problems -- Notes -- Chapter 12 Properties of the Lognormal and Normal Diffusion Processes for Modeling Assets -- 12.1 A Stochastic Process for the Asset Relative Return -- 12.2 A Stochastic Process for the Asset Price Change -- 12.3 Solving the Stochastic Differential Equation -- 12.4 Solutions to Stochastic Differential Equations Are Not Always the Same as Solutions to Corresponding Ordinary Differential Equations -- 12.5 Finding the Expected Future Asset Price -- 12.6 Geometric Brownian Motion or Arithmetic Brownian Motion? -- 12.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 13 Deriving the Black‐Scholes‐Merton Model -- 13.1 Derivation of the European Call Option Pricing Formula -- 13.2 The European Put Option Pricing Formula -- 13.3 Deriving the Black‐Scholes‐Merton Model as an Expected Value 13.4 Deriving the Black‐Scholes‐Merton Model as the Solution of a Partial Differential Equation -- 13.5 Decomposing the Black‐Scholes‐Merton Model into Binary Options -- 13.6 Black‐Scholes‐Merton Option Pricing When There Are Dividends -- 13.7 Selected Black‐Scholes‐Merton Model Limiting Results -- 13.8 Computing the Black‐Scholes‐Merton Option Pricing Model Values -- 13.9 Recap and Preview -- Appendix 13.A Deriving the Arithmetic Brownian Motion Option Pricing Model -- Questions and Problems -- Notes -- Chapter 14 The Greeks in the Black‐Scholes‐Merton Model -- 14.1 Delta: The First Derivative with Respect to the Underlying Price -- 14.2 Gamma: The Second Derivative with Respect to the Underlying Price -- 14.3 Theta: The First Derivative with Respect to Time -- 14.4 Verifying the Solution of the Partial Differential Equation -- 14.5 Selected Other Partial Derivatives of the Black‐Scholes‐Merton Model -- 14.6 Partial Derivatives of the Black‐Scholes‐Merton European Put Option Pricing Model -- 14.7 Incorporating Dividends -- 14.8 Greek Sensitivities -- 14.9 Elasticities -- 14.10 Extended Greeks of the Black‐Scholes‐Merton Option Pricing Model -- 14.11 Recap and Preview -- Questions and Problems -- Notes -- Chapter 15 Girsanov's Theorem in Option Pricing -- 15.1 The Martingale Representation Theorem -- 15.2 Introducing the Radon‐Nikodym Derivative by Changing the Drift for a Single Random Variable -- 15.3 A Complete Probability Space -- 15.4 Formal Statement of Girsanov's Theorem -- 15.5 Changing the Drift in a Continuous Time Stochastic Process -- 15.6 Changing the Drift of an Asset Price Process -- 15.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 16 Connecting Discrete and Continuous Brownian Motions -- 16.1 Brownian Motion in a Discrete World -- 16.2 Moving from a Discrete to a Continuous World 16.3 Changing the Probability Measure with the Radon‐Nikodym Derivative in Discrete Time -- 16.4 The Kolmogorov Equations -- 16.5 Recap and Preview -- Questions and Problems -- Notes -- Part IV Extensions and Generalizations of Derivative Pricing -- Chapter 17 Applying Linear Homogeneity to Option Pricing -- 17.1 Introduction to Exchange Options -- 17.2 Homogeneous Functions -- 17.3 Euler's Rule -- 17.4 Using Linear Homogeneity and Euler's Rule to Derive the Black‐Scholes‐Merton Model -- 17.5 Exchange Option Pricing -- 17.6 Spread Options3 -- 17.7 Forward Start Options -- 17.8 Recap and Preview -- Appendix 17A Linear Homogeneity and the Arithmetic Brownian Motion Model -- Appendix 17B Multivariate Itô's Lemma -- Appendix 17C Greeks of the Exchange Option Model -- Questions and Problems -- Notes -- Chapter 18 Compound Option Pricing -- 18.1 Equity as an Option -- 18.2 Valuing an Option on the Equity as a Compound Option -- 18.3 Compound Option Boundary Conditions and Parities -- 18.4 Geske's Approach to Valuing a Call on a Call -- 18.5 Characteristics of Geske's Call on Call Option -- 18.6 Geske's Call on Call Option Model and Linear Homogeneity -- 18.7 Generalized Compound Option Pricing Model -- 18.8 Installment Options -- 18.9 Recap and Preview -- Appendix 18A Selected Greeks of the Compound Option -- Questions and Problems -- Notes -- Chapter 19 American Call Option Pricing -- 19.1 Closed‐Form American Call Pricing: Roll‐Geske‐Whaley -- 19.2 The Two‐Payment Case -- 19.3 Recap and Preview -- Appendix 19A Numerical Example of the One‐Dividend Model -- Questions and Problems -- Notes -- Chapter 20 American Put Option Pricing -- 20.1 The Nature of the Problem of Pricing an American Put -- 20.2 The American Put as a Series of Compound Options -- 20.3 Recap and Preview -- Questions and Problems -- Notes -- Chapter 21 Min‐Max Option Pricing 21.1 Characteristics of Stulz's Min‐Max Option Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Preisbildung (DE-588)4047103-2 gnd rswk-swf Kapitalanlage (DE-588)4073213-7 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 s Kapitalanlage (DE-588)4073213-7 s Preisbildung (DE-588)4047103-2 s DE-604 Chance, Don M. Sonstige oth Erscheint auch als Druck-Ausgabe Brooks, Robert E. Foundations of the Pricing of Financial Derivatives Newark : John Wiley & Sons, Incorporated,c2024 9781394179657 |
| spellingShingle | Brooks, Robert E. Foundations of the Pricing of Financial Derivatives Theory and Analysis Cover -- Title Page -- Copyright -- Contents -- Preface -- Chapter 1 Introduction and Overview -- 1.1 Motivation for This Book -- 1.2 What Is a Derivative? -- 1.3 Options Versus Forwards, Futures, and Swaps -- 1.4 Size and Scope of the Financial Derivatives Markets -- 1.5 Outline and Features of the Book -- 1.6 Final Thoughts and Preview -- Questions and Problems -- Notes -- Part I Basic Foundations for Derivative Pricing -- Chapter 2 Boundaries, Limits, and Conditions on Option Prices -- 2.1 Setup, Definitions, and Arbitrage -- 2.2 Absolute Minimum and Maximum Values -- 2.3 The Value of an American Option Relative to the Value of a European Option -- 2.4 The Value of an Option at Expiration -- 2.5 The Lower Bounds of European and American Options and the Optimality of Early Exercise -- 2.6 Differences in Option Values by Exercise Price -- 2.7 The Effect of Differences in Time to Expiration -- 2.8 The Convexity Rule -- 2.9 Put‐Call Parity -- 2.10 The Effect of Interest Rates on Option Prices -- 2.11 The Effect of Volatility on Option Prices -- 2.12 The Building Blocks of European Options -- 2.13 Recap and Preview -- Questions and Problems -- Notes -- Chapter 3 Elementary Review of Mathematics for Finance -- 3.1 Summation Notation -- 3.2 Product Notation -- 3.3 Logarithms and Exponentials -- 3.4 Series Formulas -- 3.5 Calculus Derivatives -- 3.6 Integration -- 3.7 Differential Equations -- 3.8 Recap and Preview -- Questions and Problems -- Notes -- Chapter 4 Elementary Review of Probability for Finance -- 4.1 Marginal, Conditional, and Joint Probabilities -- 4.2 Expectations, Variances, and Covariances of Discrete Random Variables -- 4.3 Continuous Random Variables -- 4.4 Some General Results in Probability Theory -- 4.5 Technical Introduction to Common Probability Distributions Used in Finance -- 4.6 Recap and Preview -- Questions and Problems Notes -- Chapter 5 Financial Applications of Probability Distributions -- 5.1 The Univariate Normal Probability Distribution -- 5.2 Contrasting the Normal with the Lognormal Probability Distribution -- 5.3 Bivariate Normal Probability Distribution -- 5.4 The Bivariate Lognormal Probability Distribution -- 5.5 Recap and Preview -- Appendix 5A An Excel Routine for the Bivariate Normal Probability -- Questions and Problems -- Notes -- Chapter 6 Basic Concepts in Valuing Risky Assets and Derivatives -- 6.1 Valuing Risky Assets -- 6.2 Risk‐Neutral Pricing in Discrete Time -- 6.3 Identical Assets and the Law of One Price -- 6.4 Derivative Contracts -- 6.5 A First Look at Valuing Options -- 6.6 A World of Risk‐Averse and Risk‐Neutral Investors -- 6.7 Pricing Options Under Risk Aversion -- 6.8 Recap and Preview -- Questions and Problems -- Notes -- Part II Discrete Time Derivatives Pricing Theory -- Chapter 7 The Binomial Model -- 7.1 The One‐Period Binomial Model for Calls -- 7.2 The One‐Period Binomial Model for Puts -- 7.3 Arbitraging Price Discrepancies -- 7.4 The Multiperiod Model -- 7.5 American Options and Early Exercise in the Binomial Framework -- 7.6 Dividends and Recombination -- 7.7 Path Independence and Path Dependence -- 7.8 Recap and Preview -- Appendix 7A Derivation of Equation (7.9) -- Appendix 7B Pascal's Triangle and the Binomial Model -- Questions and Problems -- Notes -- Chapter 8 Calculating the Greeks in the Binomial Model -- 8.1 Standard Approach -- 8.2 An Enhanced Method for Estimating Delta and Gamma -- 8.3 Numerical Examples -- 8.4 Dividends -- 8.5 Recap and Preview -- Questions and Problems -- Notes -- Chapter 9 Convergence of the Binomial Model to the Black‐Scholes‐Merton Model -- 9.1 Setting Up the Problem -- 9.2 The Hsia Proof -- 9.3 Put Options -- 9.4 Dividends -- 9.5 Recap and Preview -- Questions and Problems -- Notes Part III Continuous Time Derivatives Pricing Theory -- Chapter 10 The Basics of Brownian Motion and Wiener Processes -- 10.1 Brownian Motion -- 10.2 The Wiener Process -- 10.3 Properties of a Model of Asset Price Fluctuations -- 10.4 Building a Model of Asset Price Fluctuations -- 10.5 Simulating Brownian Motion and Wiener Processes -- 10.6 Formal Statement of Wiener Process Properties -- 10.7 Recap and Preview -- Appendix 10A Simulation of the Wiener Process and the Square of the Wiener Process for Successively Smaller Time Intervals -- Questions and Problems -- Notes -- Chapter 11 Stochastic Calculus and Itô's Lemma -- 11.1 A Result from Basic Calculus -- 11.2 Introducing Stochastic Calculus and Itô's Lemma -- 11.3 Itô's Integral -- 11.4 The Integral Form of Itô's Lemma -- 11.5 Some Additional Cases of Itô's Lemma -- 11.6 Recap and Preview -- Appendix 11A Technical Stochastic Integral Results -- 11A.1 Selected Stochastic Integral Results -- 11A.2 General Linear Theorem -- Questions and Problems -- Notes -- Chapter 12 Properties of the Lognormal and Normal Diffusion Processes for Modeling Assets -- 12.1 A Stochastic Process for the Asset Relative Return -- 12.2 A Stochastic Process for the Asset Price Change -- 12.3 Solving the Stochastic Differential Equation -- 12.4 Solutions to Stochastic Differential Equations Are Not Always the Same as Solutions to Corresponding Ordinary Differential Equations -- 12.5 Finding the Expected Future Asset Price -- 12.6 Geometric Brownian Motion or Arithmetic Brownian Motion? -- 12.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 13 Deriving the Black‐Scholes‐Merton Model -- 13.1 Derivation of the European Call Option Pricing Formula -- 13.2 The European Put Option Pricing Formula -- 13.3 Deriving the Black‐Scholes‐Merton Model as an Expected Value 13.4 Deriving the Black‐Scholes‐Merton Model as the Solution of a Partial Differential Equation -- 13.5 Decomposing the Black‐Scholes‐Merton Model into Binary Options -- 13.6 Black‐Scholes‐Merton Option Pricing When There Are Dividends -- 13.7 Selected Black‐Scholes‐Merton Model Limiting Results -- 13.8 Computing the Black‐Scholes‐Merton Option Pricing Model Values -- 13.9 Recap and Preview -- Appendix 13.A Deriving the Arithmetic Brownian Motion Option Pricing Model -- Questions and Problems -- Notes -- Chapter 14 The Greeks in the Black‐Scholes‐Merton Model -- 14.1 Delta: The First Derivative with Respect to the Underlying Price -- 14.2 Gamma: The Second Derivative with Respect to the Underlying Price -- 14.3 Theta: The First Derivative with Respect to Time -- 14.4 Verifying the Solution of the Partial Differential Equation -- 14.5 Selected Other Partial Derivatives of the Black‐Scholes‐Merton Model -- 14.6 Partial Derivatives of the Black‐Scholes‐Merton European Put Option Pricing Model -- 14.7 Incorporating Dividends -- 14.8 Greek Sensitivities -- 14.9 Elasticities -- 14.10 Extended Greeks of the Black‐Scholes‐Merton Option Pricing Model -- 14.11 Recap and Preview -- Questions and Problems -- Notes -- Chapter 15 Girsanov's Theorem in Option Pricing -- 15.1 The Martingale Representation Theorem -- 15.2 Introducing the Radon‐Nikodym Derivative by Changing the Drift for a Single Random Variable -- 15.3 A Complete Probability Space -- 15.4 Formal Statement of Girsanov's Theorem -- 15.5 Changing the Drift in a Continuous Time Stochastic Process -- 15.6 Changing the Drift of an Asset Price Process -- 15.7 Recap and Preview -- Questions and Problems -- Notes -- Chapter 16 Connecting Discrete and Continuous Brownian Motions -- 16.1 Brownian Motion in a Discrete World -- 16.2 Moving from a Discrete to a Continuous World 16.3 Changing the Probability Measure with the Radon‐Nikodym Derivative in Discrete Time -- 16.4 The Kolmogorov Equations -- 16.5 Recap and Preview -- Questions and Problems -- Notes -- Part IV Extensions and Generalizations of Derivative Pricing -- Chapter 17 Applying Linear Homogeneity to Option Pricing -- 17.1 Introduction to Exchange Options -- 17.2 Homogeneous Functions -- 17.3 Euler's Rule -- 17.4 Using Linear Homogeneity and Euler's Rule to Derive the Black‐Scholes‐Merton Model -- 17.5 Exchange Option Pricing -- 17.6 Spread Options3 -- 17.7 Forward Start Options -- 17.8 Recap and Preview -- Appendix 17A Linear Homogeneity and the Arithmetic Brownian Motion Model -- Appendix 17B Multivariate Itô's Lemma -- Appendix 17C Greeks of the Exchange Option Model -- Questions and Problems -- Notes -- Chapter 18 Compound Option Pricing -- 18.1 Equity as an Option -- 18.2 Valuing an Option on the Equity as a Compound Option -- 18.3 Compound Option Boundary Conditions and Parities -- 18.4 Geske's Approach to Valuing a Call on a Call -- 18.5 Characteristics of Geske's Call on Call Option -- 18.6 Geske's Call on Call Option Model and Linear Homogeneity -- 18.7 Generalized Compound Option Pricing Model -- 18.8 Installment Options -- 18.9 Recap and Preview -- Appendix 18A Selected Greeks of the Compound Option -- Questions and Problems -- Notes -- Chapter 19 American Call Option Pricing -- 19.1 Closed‐Form American Call Pricing: Roll‐Geske‐Whaley -- 19.2 The Two‐Payment Case -- 19.3 Recap and Preview -- Appendix 19A Numerical Example of the One‐Dividend Model -- Questions and Problems -- Notes -- Chapter 20 American Put Option Pricing -- 20.1 The Nature of the Problem of Pricing an American Put -- 20.2 The American Put as a Series of Compound Options -- 20.3 Recap and Preview -- Questions and Problems -- Notes -- Chapter 21 Min‐Max Option Pricing 21.1 Characteristics of Stulz's Min‐Max Option Derivat Wertpapier (DE-588)4381572-8 gnd Preisbildung (DE-588)4047103-2 gnd Kapitalanlage (DE-588)4073213-7 gnd |
| subject_GND | (DE-588)4381572-8 (DE-588)4047103-2 (DE-588)4073213-7 |
| title | Foundations of the Pricing of Financial Derivatives Theory and Analysis |
| title_auth | Foundations of the Pricing of Financial Derivatives Theory and Analysis |
| title_exact_search | Foundations of the Pricing of Financial Derivatives Theory and Analysis |
| title_full | Foundations of the Pricing of Financial Derivatives Theory and Analysis |
| title_fullStr | Foundations of the Pricing of Financial Derivatives Theory and Analysis |
| title_full_unstemmed | Foundations of the Pricing of Financial Derivatives Theory and Analysis |
| title_short | Foundations of the Pricing of Financial Derivatives |
| title_sort | foundations of the pricing of financial derivatives theory and analysis |
| title_sub | Theory and Analysis |
| topic | Derivat Wertpapier (DE-588)4381572-8 gnd Preisbildung (DE-588)4047103-2 gnd Kapitalanlage (DE-588)4073213-7 gnd |
| topic_facet | Derivat Wertpapier Preisbildung Kapitalanlage |
| work_keys_str_mv | AT brooksroberte foundationsofthepricingoffinancialderivativestheoryandanalysis AT chancedonm foundationsofthepricingoffinancialderivativestheoryandanalysis |