Monte Carlo simulation with applications to finance /

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"Preface This book can serve as the text for a one-semester course on Monte Carlo simulation. The intended audience is advanced undergraduate students or students on master's programs who wish to learn the basics of this exciting topic and its applications to finance. The book is largely s...

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Detalles Bibliográficos
Autor principal: Wang, Hui, 1976-
Formato: Libro
Lenguaje:English
Publicado: Boca Raton : CRC Press, 2012.
Colección:Chapman & Hall/CRC financial mathematics series.
Materias:
Finanzas > Modelos matemáticos.
Método Montecarlo.
Tabla de Contenidos:
  • 1. Review of Probability. Probability Space
  • Independence and Conditional Probability
  • Random Variables
  • Random Vectors
  • Conditional Distributions
  • Conditional Expectation
  • Classical Limit Theorems
  • 2. Brownian Motion. Brownian Motion
  • Running Maximum of Brownian Motion
  • Derivatives and Black-Scholes Prices
  • Multidimensional Brownian Motions
  • 3. Arbitrage Free Pricing. Arbitrage Free Principle
  • Asset Pricing with Binomial Trees
  • The Black-Scholes Model
  • 4. Monte Carlo Simulation. Basics of Monte Carlo Simulation
  • Standard Error and Confidence Interval
  • Examples of Monte Carlo Simulation
  • Summary
  • 5. Generating Random Variables. Inverse Transform Method
  • Acceptance-Rejection Method
  • Sampling from Multivariate Normal Distributions
  • 6. Variance Reduction Techniques. Antithetic Sampling
  • Control Variates
  • Stratified Sampling
  • 7. Importance Sampling. Basic Ideas of Importance Sampling
  • The Cross-Entropy Method
  • Applications to Risk Analysis
  • 8. Stochastic Calculus. Stochastic Integrals
  • It{circ}o Formula
  • Stochastic Differential Equations
  • Risk-Neutral Pricing
  • Black-Scholes Equation
  • 9. Simulation of Diffusions. Euler Scheme
  • Eliminating Discretization Error
  • Refinements of Euler Scheme
  • The Lamperti Transform
  • Numerical Examples
  • 10. Sensitivity Analysis. Commonly Used Greeks
  • Monte Carlo Simulation of Greeks
  • Appendix A: Multivariate Normal Distributions
  • Appendix B: American Option Pricing
  • Appendix C: Option Pricing Formulas.

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