Simulation Techniques in Financial Risk Management

ISBN: 978-0-471-46987-2
240 pages
April 2006
This unique resource provides simulation techniques for financial risk managers ensuring you become well versed in many recent innovations, including Gibbs sampling, the use of heavy-tailed distributions in VaR calculations, construction of volatility smile, and state space modeling. The authors illustrate key concepts with examples and case studies you can reproduce using either S-PLUS or Visual Basic and provide exercises so you can apply new concepts and test your knowledge.

Simulation Techniques in Financial Risk Management is invaluable both as a resource for risk managers in the financial and actuarial industries and as a coursebook for upper-level undergraduate and graduate courses in simulation and risk management.

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List of Figures.

List of Tables.

Preface.

1. Introduction.

1.1 Questions.

1.2 Simulation.

1.3 Examples.

1.3.2 Monte Carlo.

1.4 Stochastic Simulations.

1.5 Exercises.

2. Brownian Motions and Itô's Rule.

2.1 Introduction.

2.2 Wiener's and Itô's Processes.

2.3 Stock Price.

2.4 Itô's Formula.

2.5 Exercises.

3. Black-Scholes Model and Option Pricing .

3.1 Introduction.

3.2 One Period Binomial Model .

3.3 The Black-Scholes-Merton Equation .

3.4 Black-Scholes Formula.

3.5 Exercises.

4. Generating Random Variables.

4.1 Introduction.

4.2 Random Numbers.

4.3 Discrete Random Variables.

4.4 Acceptance-Rejection Method .

4.5 Continuous Random Variables.

4.5.1 Inverse Transform.

4.5.2 The Rejection Method.

4.5.3 Multivariate Normal.

4.6 Exercises.

5. Standard Simulations in Risk Management.

5.1 Introduction.

5.2 Scenario Analysis.

5.2.1 Value at Risk.

5.2.2 Heavy- Tailed Distribution.

5.2.3 Case Study: VaR of Dow Jones.

5.3 Standard Monte Carlo.

5.3.1 Mean, Variance, and Interval Estimation .

5.3.2 Simulating Option Prices.

5.3.3 Simulating Option Delta.

5.4 Exercises.

5.5 Appendix.

6. Variance Reduction Techniques.

6.1 Introduction.

6.2 Antithetic Variables.

6.3 Stratified Sampling

6.4 Control Variates.

6.5 Importance Sampling.

6.6 Exercises.

7. Path-Dependent Options.

7.1 Introduction.

7.2 Barrier Option.

7.3 Lookbaclc Option.

7.4 Asian Option.

7.5 American Option.

7.5.1     Simulation: Least Squares Approach.

7.5.2     Analyzing the Least Squares Approach.

7.5.3     American-Style Path-Dependent Options.

7.6 Greek Letters.

7.7 Exercises.

8. Multi-asset Options.

8.1 Introduction.

8.2 Simulating European Multi-Asset Options.

8.3 Case Study: On Estimating Basket Options.

8.4 Dimensional Reduction.

8.5 Exercises.

9. Interest Rate Models.

9.1 Introduction.

9.2 Discount Factor.

9.2.1 Time- Varying Interest Rate.

9.3  Stochastic Interest Rate Models and Their Simulations.

9.4 Options with Stochastic Interest Rate.

9.5 Exercises.

10. Markov Chain Monte Carlo Methods.

10.1 Introduction.

10.2 Bayesian Inference.

10.3 Simulating Posteriors.

10.4 Marlcov Chain Monte Carlo.

10.4.1 Gibbs Sampling.

10.4.2  Case Study: The Impact of Jumps on Dow Jones.

10.5 Metropolis- Hustings Algorithm.

10.6 Exercises.

11.1 Chapter 1.

11.2 Chapter 2.

11.3 Chapter 3.

11.4 Chapter 4.

11.5 Chapter 5.

11.6 Chapter 6.

11.7 Chapter 7.

11.8 Chapter 8.

11.9 Chapter 9.

11.10 Chapter 10.

References.

Index.

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NGAI HANG CHAN, PhD, is Chairman and Professor of Statistics of the Department of Statistics at The Chinese University of Hong Kong where he was formerly Director of the Risk Management Science Program. He is an elected Fellow of the Institute of Mathematical Statistics, the author of Time Series: Applications to Finance (Wiley), and is also the associate editor of six journals. His research interests include statistical finance, risk management, time series, econometrics, and stochastic modeling.

HOI-YING WONG, PhD, is Assistant Professor in the Risk Management Science Program of the Department of Statistics at The Chinese University of Hong Kong. His research interests include derivatives pricing, interest rate modeling, financial risk management, and statistical finance.

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• Aims at the intermediate level where readers are not assumed to have a background in risk management (RM) or finance
• Incorporates case studies throughout the book, so readers can acquire first-hand knowledge and illustrations on how simulation techniques are applied in real-life situations
• Covers many recent methods in RM that are typically not discussed in competing works (ie. in-depth analyses on simulations of exotic options, construction of volatility smile, fixed-income assets, state space modeling) in order to narrow the gap between academic development and practical application
• Introduces the notions of market, credit, and operational risk early on so that readers can immediately appreciate the complexity and importance of stress testing and its relationship to simulations
• Showcases concepts in-text while relegating technical details to the references so readers of multiple backgrounds can absorb different levels of understanding
• Discusses Bayesian influences on techniques in an effort to address that segment of the statistical community
• Employs S-PLUS® for detailed analyses and explanations so as to minimize tedious hand computations
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"…a wonderful book and strongly recommended for practitioners in the field." (Technometrics, May 2007)

"…a nice, self-contained introduction to simulation and computational techniques in finance…interesting for practitioners…a valuable source for graduate courses…" (Mathematical Reviews, 2007c)

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