Stochastic Simulation and Applications in Finance with MATLAB Programs explains the fundamentals of Monte Carlo simulation techniques, their use in the numerical resolution of stochastic differential equations and their current applications in finance. Building on an integrated approach, it provides a pedagogical treatment of the need-to-know materials in risk management and financial engineering.
The book takes readers through the basic concepts, covering the most recent research and problems in the area, including: the quadratic re-sampling technique, the Least Squared Method, the dynamic programming and Stratified State Aggregation technique to price American options, the extreme value simulation technique to price exotic options and the retrieval of volatility method to estimate Greeks. The authors also present modern term structure of interest rate models and pricing swaptions with the BGM market model, and give a full explanation of corporate securities valuation and credit risk based on the structural approach of Merton. Case studies on financial guarantees illustrate how to implement the simulation techniques in pricing and hedging.
The book also includes an accompanying CD-ROM which provides MATLAB programs for the practical examples and case studies, which will give the reader confidence in using and adapting specific ways to solve problems involving stochastic processes in finance.
Key Topics Covered:
- Chapter 1: Introduction to probability.
- Chapter 2: Introduction to random variables.
- Chapter 3: Random sequences.
- Chapter 4: Introduction to computer simulation of random variables.
- Chapter 5: Foundations of Monte Carlo simulations.
- Chapter 6: Fundamentals of Quasi Monte Carlo (QMC) simulations.
- Chapter 7: Introduction to random processes.
- Chapter 8: Solution of stochastic differential equations.
- Chapter 9: General approach to the valuation of contingent claims.
- Chapter 10: Pricing options using Monte Carlo simulations.
- Chapter 11: Term structure of interest rates and interest rate derivatives.
- Chapter 12: Credit risk and the valuation of corporate securities.
- Chapter 13: Valuation of portfolios of financial guarantees.
- Chapter 14: Risk management and Value at Risk (VaR).
- Chapter 15: VaR and Principal Components Analysis (PCA).
- Appendix A: Review of mathematics.
- Appendix B: MATLABøR Functions.
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