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Risk-Neutral Valuation

Pricing and Hedging of Financial Derivatives. 'Springer Finance Textbooks'. 2nd ed. 2004. Mit Abbildungen,…
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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... weiterlesen
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Titel: Risk-Neutral Valuation
Autor/en: Nicholas H. Bingham, Rüdiger Kiesel

ISBN: 1852334584
EAN: 9781852334581
Pricing and Hedging of Financial Derivatives.
'Springer Finance Textbooks'.
2nd ed. 2004.
Mit Abbildungen, Graf. und Tabellen.
Sprache: Englisch.
Springer-Verlag GmbH

Juni 2004 - gebunden - XVIII

Beschreibung

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.

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

Pressestimmen

Authors of financial engineering texts face a quandary: how technical to make a book? It is easy to alienate readers by being too technical, but it is just as easy to write a fluff book that communicates nothing of substance. With this book, authors Bingham and Kiesel have got the balance just right... It is mathematically rigorous but with a practical, reader-oriented focus. Results are expressed formally as mathematical theorems, but the authors skip most proofs. The narrative moves along at a nice clip so you never get bogged down in minutia... Who is the book for? Almost anyone who has a strong background in maths and wants a command of financial engineering theory. www.riskbook.com

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