A thoroughly revised and updated edition of a popular text: it brings readers completely up-to-date with recent developments in the field
Includes a new chapter on the important topic of Credit Risk, and provides additional resources for lecturers via the web
Written with the practitioner in mind, it gets straight to the heart of the subject and shows how to put the theory into practice
This second edition - completely up to date with new exercises - provides a comprehensive and self-contained treatment of the probabilistic theory behind the risk-neutral valuation principle and its application to the pricing and hedging of financial derivatives. On the probabilistic side, both discrete- and continuous-time stochastic processes are treated, with special emphasis on martingale theory, stochastic integration and change-of-measure techniques. Based on firm probabilistic foundations, general properties of discrete- and continuous-time financial market models are discussed.
|Since its introduction in the early 1980s, the risk-neutral valuation principle has proved to be an important tool in the pricing and hedging of financial derivatives. Following the success of the first edition of `Risk-Neutral Valuation´, the authors have thoroughly revised the entire book, taking into account recent developments in the field, and changes in their own thinking and teaching. In particular, the chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on: ·Infinite divisibility and Lévy processes ·Lévy-based models in incomplete markets Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers. |In this second edition of their popular text, the authors take into account recent developments in the field, and changes in their own thinking and teaching. The chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on: ·Infinite divisibility and Lévy processes ·Lévy-based models in incomplete markets Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers.
ContentsPreface to the Second Edition Preface to the First Edition 1. Derivative Background 1.1 Financial Markets and Instruments 1.1.1 Derivative Instruments 1.1.2 Underlying Securities 1.1.3 Markets 1.1.4 Types of Traders 1.1.5 Modeling Assumptions 1.2 Arbitrage1.3 Arbitrage Relationships 1.3.1 Fundamental Determinants of Option Values 1.3.2 Arbitrage Bounds 1.4 Single-period Market Models 1.4.1 A Fundamental Example 1.4.2 A Single-period Model 1.4.3 A Few Financial-economic Considerations Exercises 2. Probability Background 2.1 Measure 2.2 Integral 2.3 Probability 2.4 Equivalent Measures and Radon-Nikodym Derivatives 2.5 Conditional Expectation2.6 Modes of Convergence 2.7 Convolution and Characteristic Functions 2.8 The Central Limit Theorem 2.9 Asset Return Distributions 2.10 In.nite Divisibility and the L´evy-Khintchine Formula 2.11 Elliptically Contoured Distributions2.12 Hyberbolic Distributions Exercises 3. Stochastic Processes in Discrete Time 3.1 Information and Filtrations 3.2 Discrete-parameter Stochastic Processes 3.3 De.nition and Basic Properties of Martingales 3.4 Martingale Transforms 3.5 Stopping Times and Optional Stopping3.6 The Snell Envelope and Optimal Stopping 3.7 Spaces of Martingales 3.8 Markov Chains Exercises 4. Mathematical Finance in Discrete Time 4.1 The Model 4.2 Existence of Equivalent Martingale Measures4.2.1 The No-arbitrage Condition 4.2.2 Risk-Neutral Pricing 4.3 Complete Markets: Uniqueness of EMMs 4.4 The Fundamental Theorem of Asset Pricing: Risk-Neutral Valuation4.5 The Cox-Ross-Rubinstein Model 4.5.1 Model Structure4.5.2 Risk-neutral Pricing 4.5.3 Hedging 4.6 Binomial Approximations4.6.1 Model Structure4.6.2 The Black-Scholes Option Pricing Formula 4.6.3 Further Limiting Models4.7 American Options 4.7.1 Theory4.7.2 American Options in the CRR Model 4.8 Further Contingent Claim Valuation in Discrete Time 4.8.1 Barrier Options 4.8.2 Lookback Options 4.8.3 A Three-period Example 4.9 Multifactor Models 4.9.1 Extended Binomial Model 4.9.2 Multinomial Models Exercises 5. Stochastic Processes in Continuous Time 5.1 Filtrations; Finite-dimensional Distributions 5.2 Classes of Processes 5.2.1 Martingales 5.2.2 Gaussian Processes 5.2.3 Markov Processes 5.2.4 Diffusions 5.3 Brownian Motion 5.3.1 Definition and Existence 5.3.2 Quadratic Variation of Brownian Motion 5.3.3 Properties of Brownian Motion5.3.4 Brownian Motion in Stochastic Modeling 5.4 Point Processes 5.4.1 Exponential Distribution 5.4.2 The Poisson Process 5.4.3 Compound Poisson Processes 5.4.4 Renewal Processes 5.5 Levy Processes 5.5.1 Distributions 5.5.2 Levy Processes 5.5.3 Levy Processes and the Levy-Khintchine Formula5.6 Stochastic Integrals; Ito Calculus 5.6.1 Stochastic Integration5.6.2 Ito´s Lemma 5.6.3 Geometric Brownian Motion 5.7 Stochastic Calculus for Black-Scholes Models5.8 Stochastic Differential Equations 5.9 Likelihood Estimation for Diffusions 5.10 Martingales, Local Martingales and Semi-martingales 5.10.1 Definitions 5.10.2 Semi-martingale Calculus5.10.3 Stochastic Exponentials 5.10.4 Semi-martingale Characteristics 5.11 Weak Convergence of Stochastic Processes 5.11.1 The Spaces Cd and Dd 5.11.2 Definition and Motivation 5.11.3 Basic Theorems of Weak Convergence 5.11.4 Weak Convergence Results for Stochastic IntegralsExercises 6. Mathematical Finance in Continuous Time 6.1 Continuous-time Financial Market Models 6.1.1 The Financial Market Model 6.1.2 Equivalent Martingale Measures 6.1.3 Risk-neutral Pricing 6.1.4 Changes of Numeraire
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Since its introduction in the early 1980s, the risk-neutral valuation principle has proved to be an important tool in the pricing and hedging of financial derivatives. Following the success of the first edition of 'Risk-Neutral Valuation', the authors have thoroughly revised the entire book, taking into account recent developments in the field, and changes in their own thinking and teaching. In particular, the chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on: ·Infinite divisibility and Lévy processes ·Lévy-based models in incomplete markets Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers.
1. Derivative Background.- 2. Probability Background.- 3. Stochastic Processes in Discrete Time.- 4. Mathematical Finance in Discrete Time.- 5. Stochastic Processes in Continuous Time.- 6. Mathematical Finance in Continuous Time.- 7. Incomplete Markets.- 8. Interest Rate Theory.- 9. Credit Risk.- A. Hilbert Space.- B. Projections and Conditional Expectations.- C. The Separating Hyperplane Theorem.
Inhaltsverzeichnis
Contents
Preface to the Second Edition
Preface to the First Edition
1. Derivative Background
1.1 Financial Markets and Instruments
1.1.1 Derivative Instruments
1.1.2 Underlying Securities
1.1.3 Markets
1.1.4 Types of Traders
1.1.5 Modeling Assumptions
1.2 Arbitrage
1.3 Arbitrage Relationships
1.3.1 Fundamental Determinants of Option Values
1.3.2 Arbitrage Bounds
1.4 Single-period Market Models
1.4.1 A Fundamental Example
1.4.2 A Single-period Model
1.4.3 A Few Financial-economic Considerations
Exercises 2. Probability Background
2.1 Measure
2.2 Integral
2.3 Probability
2.4 Equivalent Measures and Radon-Nikodym Derivatives
2.5 Conditional Expectation
2.6 Modes of Convergence
2.7 Convolution and Characteristic Functions
2.8 The Central Limit Theorem
2.9 Asset Return Distributions
2.10 In.nite Divisibility and the L¿evy-Khintchine Formula
2.11 Elliptically Contoured Distributions
2.12 Hyberbolic Distributions
Exercises 3. Stochastic Processes in Discrete Time
3.1 Information and Filtrations
3.2 Discrete-parameter Stochastic Processes
3.3 De.nition and Basic Properties of Martingales
3.4 Martingale Transforms
3.5 Stopping Times and Optional Stopping
3.6 The Snell Envelope and Optimal Stopping
3.7 Spaces of Martingales
3.8 Markov Chains
Exercises 4. Mathematical Finance in Discrete Time
4.1 The Model
4.2 Existence of Equivalent Martingale Measures
4.2.1 The No-arbitrage Condition
4.2.2 Risk-Neutral Pricing
4.3 Complete Markets: Uniqueness of EMMs
4.4 The Fundamental Theorem of Asset Pricing: Risk-Neutral Valuation
4.5 The Cox-Ross-Rubinstein Model
4.5.1 Model Structure
4.5.2 Risk-neutral Pricing
4.5.3 Hedging
4.6 Binomial Approximations
4.6.1 Model Structure
4.6.2 The Black-Scholes Option Pricing Formula
4.6.3 Further Limiting Models
4.7 American Options
4.7.1 Theory
4.7.2 American Options in the CRR Model
4.8 Further Contingent Claim Valuation in Discrete Time
4.8.1 Barrier Options
4.8.2 Lookback Options
4.8.3 A Three-period Example
4.9 Multifactor Models
4.9.1 Extended Binomial Model
4.9.2 Multinomial Models
Exercises 5. Stochastic Processes in Continuous Time
5.1 Filtrations; Finite-dimensional Distributions
5.2 Classes of Processes
5.2.1 Martingales
5.2.2 Gaussian Processes
5.2.3 Markov Processes
5.2.4 Diffusions
5.3 Brownian Motion
5.3.1 Definition and Existence
5.3.2 Quadratic Variation of Brownian Motion
5.3.3 Properties of Brownian Motion
5.3.4 Brownian Motion in Stochastic Modeling
5.4 Point Processes
5.4.1 Exponential Distribution
5.4.2 The Poisson Process
5.4.3 Compound Poisson Processes
5.4.4 Renewal Processes
5.5 Levy Processes
5.5.1 Distributions
5.5.2 Levy Processes
5.5.3 Levy Processes and the Levy-Khintchine Formula
5.6 Stochastic Integrals; Ito Calculus
5.6.1 Stochastic Integration
5.6.2 Ito's Lemma
5.6.3 Geometric Brownian Motion
5.7 Stochastic Calculus for Black-Scholes Models
5.8 Stochastic Differential Equations
5.9 Likelihood Estimation for Diffusions
5.10 Martingales, Local Martingales and Semi-martingales
5.10.1 Definitions
5.10.2 Semi-martingale Calculus
5.10.3 Stochastic Exponentials
5.10.4 Semi-martingale Characteristics
5.11 Weak Convergence of Stochastic Processes
5.11.1 The Spaces Cd and Dd
5.11.2 Definition and Motivation
5.11.3 Basic Theorems of Weak Convergence
5.11.4 Weak Convergence Results for Stochastic Integrals
Exercises 6. Mathematical Finance in Continuous Time
6.1 Continuous-time Financial Market Models
6.1.1 The Financial Market Model
6.1.2 Equivalent Martingale Measures
6.1.3 Risk-neutral Pricing
6.1.4 Changes of Numeraire
Klappentext
Since its introduction in the early 1980s, the risk-neutral valuation principle has proved to be an important tool in the pricing and hedging of financial derivatives.
Following the success of the first edition of ¿Risk-Neutral Valuation¿, the authors have thoroughly revised the entire book, taking into account recent developments in the field, and changes in their own thinking and teaching.
In particular, the chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on:
· Infinite divisibility and Lévy processes
· Lévy-based models in incomplete markets
Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers.
In this second edition of their popular text, the authors take into account recent developments in the field, and changes in their own thinking and teaching.
The chapters on Incomplete Markets and Interest Rate Theory have been updated and extended, there is a new chapter on the important and growing area of Credit Risk and, in recognition of the increasing popularity of Lévy finance, there is considerable new material on:
·Infinite divisibility and Lévy processes
·Lévy-based models in incomplete markets
Further material such as exercises, solutions to exercises and lecture slides are also available via the web to provide additional support for lecturers.
