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.
"This book provides a very useful set of tools for those who are interested in the simulation method of asset pricing and its implementation with MatLab. It is pitched at just the right level for anyone who seeks to learn about this fascinating area of finance. The collection of specific topics thoughtfully selected by the authors, such as credit risk, loan guarantee and value-at-risk, is an additional nice feature, making it a great source of reference for researchers and practitioners. The book is a valuable contribution to the fast growing area of quantitative finance."
-Tan Wang, Sauder School of Business, UBC
“This book is a good companion to text books on theory, so if you want to get straight to the meat of implementing the classical quantitative finance models here's the answer.”
—Paul Wilmott, wilmott.com
“This powerful book is a comprehensive guide for Monte Carlo methods in finance. Every quant knows that one of the biggest issues in finance is to well understand the mathematical framework in order to translate it in programming code. Look at the chapter on Quasi Monte Carlo or the paragraph on variance reduction techniques and you will see that Huu Tue Huynh, Van Son Lai and Issouf Soumare have done a very good job in order to provide a bridge between the complex mathematics used in finance and the programming implementation. Because it adopts both theoretical and practical point of views with a lot of applications, because it treats about some sophisticated financial problems (like Brownian bridges, jump processes, exotic options pricing or Longstaff-Schwartz methods) and because it is easy to understand, this handbook is valuable for academics, students and financial engineers who want to learn the computational aspects of simulations in finance.”
—Thierry Roncalli, Head of Investment Products and Strategies, SGAM Alternative Investments & Professor of Finance, University of Evry
Chapter 1 Introduction to Probability (pages 1–7):
Chapter 2 Introduction to Random Variables (pages 9–37):
Chapter 3 Random Sequences (pages 39–46):
Chapter 4 Introduction to Computer Simulation of Random Variables (pages 47–66):
Chapter 5 Foundations of Monte Carlo Simulations (pages 67–90):
Chapter 6 Fundamentals of Quasi Monte Carlo (QMC) Simulations (pages 91–107):
Chapter 7 Introduction to Random Processes (pages 109–122):
Chapter 8 Solution of Stochastic Differential Equations (pages 123–148):
Chapter 9 General Approach to the Valuation of Contingent Claims (pages 149–167):
Chapter 10 Pricing Options using Monte Carlo Simulations (pages 169–219):
Chapter 11 Term Structure of Interest Rates and Interest Rate Derivatives (pages 221–246):
Chapter 12 Credit Risk and the Valuation of Corporate Securities (pages 247–264):
Chapter 13 Valuation of Portfolios of Financial Guarantees (pages 265–281):
Chapter 14 Risk Management and Value at Risk (VaR) (pages 283–295):
Chapter 15 Value at Risk (VaR) and Principal Components Analysis (PCA) (pages 297–313):