An authoritative handbook on risk management techniques and
simulations as applied to financial engineering topics, theories,
and statistical methodologies



The Handbook of Financial Risk Management: Simulations and Case
Studies illustrates the prac-tical implementation of
simulation techniques in the banking and financial industries
through the use of real-world applications.

Striking a balance between theory and practice, the Handbook
of Financial Risk Management: Simulations and Case Studies
demonstrates how simulation algorithms can be used to solve
practical problems and showcases how accuracy and efficiency in
implementing various simulation methods are indispensable tools in
risk management. The book provides the reader with an intuitive
understanding of financial risk management and deepens insight into
those financial products that cannot be priced traditionally. The
Handbook of Financial Risk Management also features:

* Examples in each chapter derived from consulting projects,
current research, and course instruction

* Topics such as volatility, fixed-income derivatives, LIBOR
Market Models, and risk measures

* Over twenty-four recognized simulation models

* Commentary, data sets, and computer subroutines available on a
chapter-by-chapter basis

As a complete reference for practitioners, the book is useful in
the fields of finance, business, applied statistics, econometrics,
and engineering. The Handbook of Financial Risk Management
is also an excellent text or supplement for graduate and MBA-level
students in courses on financial risk management and
simulation.

N. H. CHAN is Choh-Ming Li Chair Professor of Statistics
at The Chinese University of Hong Kong and Associate Editor of six
journals. Dr. Chan is also the author of Time Series:
Applications to Finance with R and S-Plus, Second Edition,
published by Wiley.

H. Y. WONG is Associate Professor in the Risk Management
Science Program of the Department of Statistics at The Chinese
University of Hong Kong. His areas of interest include data
analysis, statistical computing, risk management, and stochastic
calculus.

An authoritative handbook on risk management techniques and simulations as applied to financial engineering topics, theories, and statistical methodologies

The Handbook of Financial Risk Management: Simulations and Case Studies illustrates the prac­tical implementation of simulation techniques in the banking and financial industries through the use of real-world applications.

Striking a balance between theory and practice, the Handbook of Financial Risk Management: Simulations and Case Studies demonstrates how simulation algorithms can be used to solve practical problems and showcases how accuracy and efficiency in implementing various simulation methods are indispensable tools in risk management. The book provides the reader with an intuitive understanding of financial risk management and deepens insight into those financial products that cannot be priced traditionally. The Handbook of Financial Risk Management also features:

• Examples in each chapter derived from consulting projects, current research, and course instruction
• Topics such as volatility, fixed-income derivatives, LIBOR Market Models, and risk measures
• Over twenty-four recognized simulation models
• Commentary, data sets, and computer subroutines available on a chapter-by-chapter basis

As a complete reference for practitioners, the book is useful in the fields of finance, business, applied statistics, econometrics, and engineering. The Handbook of Financial Risk Management is also an excellent text or supplement for graduate and MBA-level students in courses on financial risk management and simulation.

List of Figures x

List of Tables xiv

Preface xx

1 An Introduction to Excel VBA 1

1.1 How to start Excel VBA 1

1.2 VBA Programming Fundamentals 3

1.3 Linking VBA to C++ 14

1.5 Random Number Generation 19

1.6 List of functions defined in the book 22

2 Background 27

2.1 A brief review of Martingales and Itô's calculus
28

2.2 Volatility 39

2.3 Mark to Market and Calibration 41

2.4 Variance Reduction Techniques 43

3 Structured Products 55

3.1 When is simulation unnecessary? 55

3.2 Simulation of Black-Scholes model and European Options
56

3.3 American Options 61

3.4 Range Accrual Notes 69

3.5 FX accumulator: The case of Citic Pacific LTD 73

3.6 Life Insurance Contracts 80

3.7 Multi-asset Instruments 83

4 Volatility Modeling 93

4.1 Local Volatility Models: Simulation and Binomial tree 94

4.2 The Heston Stochastic Volatility Model 104

4.3 Simulation of Exotic Option Prices under Heston Model
110

4.4 The GARCH Option Pricing Model 121

4.5 Jump-Diffusion Model 127

5 Fixed-Income Derivatives I: Short-Rate Models 137

5.1 Yield Curve Building 138

5.2 The Hull-White Model 150

5.3 Pricing Interest Rate Products Using The Direction
Simulation Approach 156

5.4 Pricing Interest Rate Products Using The Trinomial Tree
Approach 161

6 Fixed-Income Derivatives II: LIBOR Market Models
169

6.1 LIBOR Market Models 171

6.2 Calibration to Caps and Swaptions 177

6.3 Simulation Across Different Forward Measures 186

6.4 Bermudan Swaptions in a Three-Factor Model 194

6.5 Epilogue 196

7 Credit Derivatives and Counterparty Credit Risk 199

7.1 Structural Models of Credit Risk 200

7.2 The Vasicek Single-Factor Model 203

7.3 Copula Approach to Credit Derivative Pricing 212

7.4 Counterparty credit risk 223

8 Value-at-Risk and Related Risk Measures 237

8.1 Value-at-Risk 237

8.2 Parametric VaR 238

8.3 Delta-normal Approximation 245

8.4 Delta-Gamma Approximation 247

8.5 VaR Simulation Methods 249

8.6 VaR-related Risk Measures 258

8.7 VaR Back-testing 264

9 The Greeks 267

9.1 Black-Scholes Greeks 269

9.2 Greeks in A Binomial Tree 271

9.3 Finite Difference Approximation 272

9.4 Likelihood Ratio Method 276

9.5 Pathwise Derivative Estimates 279

9.6 Greek Calculation with Discontinuous Payoffs 289

10 Appendix 295

References 315

Subject Index 319

Author Index 323