Risk-Neutral Valuation

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69,54 

Pricing and Hedging of Financial Derivatives, Springer Finance – Springer Finance Textbooks

ISBN: 184996873X
ISBN 13: 9781849968737
Autor: Bingham, Nicholas H/Kiesel, Rüdiger
Verlag: Springer Verlag GmbH
Umfang: xviii, 438 S.
Erscheinungsdatum: 21.10.2010
Auflage: 2/2004
Produktform: Kartoniert
Einband: KT

2nd edition

A thoroughly revised and updated edition of a popular text: it brings readers completely up-to-date with recent developments in the fieldIncludes a new chapter on the important topic of Credit Risk, and provides additional resources for lecturers via the webWritten with the practitioner in mind, it gets straight to the heart of the subject and shows how to put the theory into practiceIncludes supplementary material: sn.pub/extrasRequest lecturer material: sn.pub/lecturer-material

Artikelnummer: 958692 Kategorie:

Beschreibung

InhaltsangabeContents 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 Singleperiod 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 Discreteparameter 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 Noarbitrage Condition 4.2.2 RiskNeutral Pricing 4.3 Complete Markets: Uniqueness of EMMs 4.4 The Fundamental Theorem of Asset Pricing: Risk-Neutral Valuation 4.5 The CoxRossRubinstein Model 4.5.1 Model Structure 4.5.2 Riskneutral 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 Semimartingale Calculus 5.10.3 Stochastic Exponentials 5.10.4 Semimartingale 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 Riskneutral Pricing 6.1.4 Changes of Numeraire

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 6.2 The Generalized Black-Scholes Model 6.2.1 The Model 6.2.2 Pricing and Hedging Contingen ...

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