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Description of Monte Carlo Methods in Financial Engineering: v. 53 |
Monte Carlo simulation has become an essential tool in the pricing of derivative securities and in risk management. These applications have, in turn, stimulated research into new Monte Carlo methods and renewed interest in some older techniques. This book develops the use of Monte Carlo methods in finance and it also uses simulation as a vehicle for presenting models and ideas from financial engineering. It divides roughly into three parts. The first part develops the fundamentals of Monte Carlo methods, the foundations of derivatives pricing, and the implementation of several of the most important models used in financial engineering. The next part describes techniques for improving simulation accuracy and efficiency.The final third of the book addresses special topics: estimating price sensitivities, valuing American options, and measuring market risk and credit risk in financial portfolios. The most important prerequisite is familiarity with the mathematical tools used to specify and analyze continuous-time models in finance, in particular the key ideas of stochastic calculus. Prior exposure to the basic principles of option pricing is useful but not essential.
The book is aimed at graduate students in financial engineering, researchers in Monte Carlo simulation, and practitioners implementing models in industry. "Mathematical Reviews", 2004 - '...this book is very comprehensive, up-to-date and useful tool for those who are interested in implementing Monte Carlo methods in a financial context'.
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Contents of Monte Carlo Methods in Financial Engineering: v. 53 |
1. Foundations
Principles of Monte Carlo
Principles of Derivatives Pricing
2. Generating Random Numbers and Random Variables
Random Number Generation
General Sampling Methods
Normal Random Variables and Vectors
3. Generating Sample Paths
Brownian Motion
Gaussian Short Rate Models
Square-Root Diffusions
Processes with Jump
Forward Rate Models: Continuous Rates
Forward Rate Models: Simple Rates
4. Variance Reduction Techniques
Control Variates
Antithetic Variates
Stratified Sampling
Latin Hypercube Sampling
Matching Underlying Assets
Importance Sampling
Concluding Remarks
5. Quasi-Monte Carlo Methods
General Principles
Low-Discrepancy Sequences
Lattice Rules
Randomized QMC
The Finance Setting
Concluding Remarks
6. Discretization Methods
Introduction
Second-Order Methods
Extensions
Extremes and Barrier Crossings: Brownian Interpolation
Changing Variables
Concluding Remarks
7. Estimating Sensitivities
Finite-Difference Approximations
Pathwise Derivative Estimates
The Likelihood Ratio Method
Concluding Remarks
8. Pricing American Options
Problem Formulation
Parametric Approximations
Random Tree Methods
State-Space Partitioning
Stochastic Mesh Methods
Regression-Based Methods and Weights
Duality
Concluding Remarks
9. Applications in Risk Management
Loss Probabilities and Value-at-Risk
Variance Reduction Using the Delta-Gamma Approximation
A Heavy-Tailed Setting
Credit Risk
Concluding Remarks
A Appendix: Convergence and Confidence Intervals
B Appendix: Results from Stochastic Calculus
C Appendix: The Term Structure of Interest Rates
References
Index
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