Simulation Techniques in Financial Risk Management

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.

List of Figures. List of Tables. Preface. 1. Introduction. 1.1 Questions. 1.2 Simulation. 1.3 Examples. 1.3.1 Quadrature. 1.3.2 Monte Carlo. 1.4 Stochastic Simulations. 1.5 Exercises. 2. Brownian Motions and Ito's Rule. 2.1 Introduction. 2.2 Wiener's and Ito's Processes. 2.3 Stock Price. 2.4 Ito'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. Answers to Selected 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.