Stochastic financial models /

Stochastic financial models /

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Bibliographic Details
Author / Creator:Kennedy, Douglas.
Imprint:Boca Raton, FL : Chapman & Hall/CRC, c2010.
Description:257 p. : ill. ; 25 cm.
Language:English
Series:Chapman & Hall/CRC financial mathematics series
Chapman & Hall/CRC financial mathematics series.
Subject:
Investments -- Mathematical models.
Stochastic analysis.
Investments -- Mathematical models.
Stochastic analysis.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/7979583
Hidden Bibliographic Details
ISBN:9781420093452 (hardcover : alk. paper)
1420093452 (hardcover : alk. paper)
Notes:Includes bibliographical references and index.
Table of Contents:
  • Preface
  • 1. Portfolio Choice
  • 1.1. Introduction
  • 1.2. Utility
  • 1.2.1. Preferences and utility
  • 1.2.2. Utility and risk aversion
  • 1.3. Mean-variance analysis
  • 1.3.1. Introduction
  • 1.3.2. All risky assets
  • 1.3.3. A riskless asset
  • 1.3.4. Mean-variance analysis and expected utility
  • 1.3.5. Equilibrium: the capital-asset pricing model
  • 1.4. Exercises
  • 2. The Binomial Model
  • 2.1. One-period model
  • 2.1.1. Introduction
  • 2.1.2. Hedging
  • 2.1.3. Arbitrage
  • 2.1.4. Utility maximization
  • 2.2. Multi-period model
  • 2.2.1. Introduction
  • 2.2.2. Dynamic hedging
  • 2.2.3. Change of probability
  • 2.2.4. Utility maximization
  • 2.2.5. Path-dependent claims
  • 2.2.6. American claims
  • 2.2.7. The non-standard multi-period model
  • 2.3. Exercises
  • 3. A General Discrete-Time Model
  • 3.1. One-period model
  • 3.1.1. Introduction
  • 3.1.2. Arbitrage
  • 3.2. Multi-period model
  • 3.2.1. Introduction
  • 3.2.2. Pricing claims
  • 3.3. Exercises
  • 4. Brownian Motion
  • 4.1. Introduction
  • 4.2. Hitting-time distributions
  • 4.2.1. The reflection principle
  • 4.2.2. Transformations of Brownian motion
  • 4.2.3. Computations using martingales
  • 4.3. Girsanov's Theorem
  • 4.4. Brownian motion as a limit
  • 4.5. Stochastic calculus
  • 4.6. Exercises
  • 5. The Black-Scholes Model
  • 5.1. Introduction
  • 5.2. The Black-Scholes formula
  • 5.2.1. Derivation
  • 5.2.2. Dependence on the parameters: the Greeks
  • 5.2.3. Volatility
  • 5.3. Hedging and the Black-Scholes equation
  • 5.3.1. Self-financing portfolios
  • 5.3.2. Dividend-paying claims
  • 5.3.3. General terminal-value claims
  • 5.3.4. Specific terminal-value claims
  • 5.3.5. Utility maximization
  • 5.3.6. American claims
  • 5.4. Path-dependent claims
  • 5.4.1. Forward-start and lookback options
  • 5.4.2. Barrier options
  • 5.5. Dividend-paying assets
  • 5.6. Exercises
  • 6. Interest-Rate Models
  • 6.1. Introduction
  • 6.2. Survey of interest-rate models
  • 6.2.1. One-factor models
  • 6.2.2. Forward-rate and market models
  • 6.3. Gaussian random-field model
  • 6.3.1. Introduction
  • 6.3.2. Pricing a caplet on forward rates
  • 6.3.3. Markov properties
  • 6.3.4. Finite-factor models and restricted information
  • 6.4. Exercises
  • A. Mathematical Preliminaries
  • A.1. Probability background
  • A.1.1. Probability spaces
  • A.1.2. Conditional expectations
  • A.1.3. Change of probability
  • A.1.4. Essential supremum
  • A.2. Martingales
  • A.3. Gaussian random variables
  • A.3.1. Univariate normal distributions
  • A.3.2. Multivariate normal distributions
  • A.4. Convexity
  • B. Solutions to the Exercises
  • B.1. Portfolio Choice
  • B.2. The Binomial Model
  • B.3. A General Discrete-Time Model
  • B.4. Brownian Motion
  • B.5. The Black-Scholes Model
  • B.6. Interest-Rate Models
  • Further Reading
  • References
  • Index
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