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    Broschiertes Buch

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.…mehr

Produktbeschreibung
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.
  • Produktdetails
  • Springer Finance
  • Verlag: Springer / Springer, Berlin / Springer, London
  • 2nd ed.
  • Seitenzahl: 456
  • Erscheinungstermin: 21. Oktober 2010
  • Englisch
  • Abmessung: 235mm x 155mm x 24mm
  • Gewicht: 686g
  • ISBN-13: 9781849968737
  • ISBN-10: 184996873X
  • Artikelnr.: 32208840
Inhaltsangabe
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
Rezensionen
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
"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