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Monte Carlo simulation with applications to finance /
"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...
| Autor principal: | |
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| Formato: | Libro |
| Lenguaje: | English |
| Publicado: |
Boca Raton :
CRC Press,
2012.
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| Colección: | Chapman & Hall/CRC financial mathematics series.
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| Materias: |
MARC
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| 100 | 1 | |a Wang, Hui, |d 1976- | |
| 245 | 1 | 0 | |a Monte Carlo simulation with applications to finance / |c Hui Wang. |
| 260 | |a Boca Raton : |b CRC Press, |c 2012. | ||
| 300 | |a ix, 282 p. : |b il. ; |c 24 cm. | ||
| 490 | 1 | |a Chapman & Hall/CRC financial mathematics series | |
| 504 | |a Incluye bibliografía (p. [277]-279) e índice. | ||
| 505 | 0 | |a 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. | |
| 520 | |a "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 self-contained. The only prerequisite is some experience with probability and statistics. Prior knowledge on option pricing is helpful but not essential. As in any study of Monte Carlo simulation, coding is an integral part and cannot be ignored. The book contains a large number of MATLAB coding exercises. They are designed in a progressive manner so that no prior experience with MATLAB is required. Much of the mathematics in the book is informal. For example, randomvariables are simply defined to be functions on the sample space, even though they should be measurable with respect to appropriate algebras; exchanging the order of integrations is carried out liberally, even though it should be justified by the Tonelli-Fubini Theorem. The motivation for doing so is to avoid the technical measure theoretic jargon, which is of little concern in practice and does not help much to further the understanding of the topic. The book is an extension of the lecture notes that I have developed for an undergraduate course on Monte Carlo simulation at Brown University. I would like to thank the students who have taken the course, as well as the Division of Applied Mathematics at Brown, for their support. Hui Wang Providence, Rhode Island January, 2012"-- |c Provided by publisher. | ||
| 650 | 4 | |a Finanzas |x Modelos matemáticos. | |
| 650 | 4 | |a Método Montecarlo. | |
| 830 | 0 | |a Chapman & Hall/CRC financial mathematics series. | |
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