Handbook of Financial Risk Management Simulations and Case Studies

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