Advanced Modelling in Finance using Excel and VBA

Preface xi

Acknowledgements xii

1 Introduction 1

1.1 Finance insights 1

1.2 Asset price assumptions 2

1.3 Mathematical and statistical problems 2

1.4 Numerical methods 2

1.5 Excel solutions 3

1.6 Topics covered 3

1.7 Related Excel workbooks 5

1.8 Comments and suggestions 5

Part One Advanced Modelling in Excel 7

2 Advanced Excel functions and procedures 9

2.1 Accessing functions in Excel 9

2.2 Mathematical functions 10

2.3 Statistical functions 12

2.3.1 Using the frequency function 12

2.3.2 Using the quartile function 14

2.3.3 Using Excel’s normal functions 15

2.4 Lookup functions 16

2.5 Other functions 18

2.6 Auditing tools 19

2.7 Data Tables 20

2.7.1 Setting up Data Tables with one input 20

2.7.2 Setting up Data Tables with two inputs 22

2.8 XY charts 23

2.9 Access to Data Analysis and Solver 26

2.10 Using range names 27

2.11 Regression 28

2.12 Goal Seek 31

2.13 Matrix algebra and related functions 33

2.13.1 Introduction to matrices 33

2.13.2 Transposing a matrix 33

2.13.3 Adding matrices 34

2.13.4 Multiplying matrices 34

2.13.5 Matrix inversion 35

2.13.6 Solving systems of simultaneous linear equations 36

2.13.7 Summary of Excel’s matrix functions 37

Summary 37

3 Introduction to VBA 39

3.1 Advantages of mastering VBA 39

3.2 Object-oriented aspects of VBA 40

3.3 Starting to write VBA macros 42

3.3.1 Some simple examples of VBA subroutines 42

3.3.2 MsgBox for interaction 43

3.3.3 The writing environment 44

3.3.4 Entering code and executing macros 44

3.3.5 Recording keystrokes and editing code 45

3.4 Elements of programming 47

3.4.1 Variables and data types 48

3.4.2 VBA array variables 48

3.4.3 Control structures 50

3.4.4 Control of repeating procedures 51

3.4.5 Using Excel functions and VBA functions in code 52

3.4.6 General points on programming 53

3.5 Communicating between macros and the spreadsheet 53

3.6 Subroutine examples 56

3.6.1 Charts 56

3.6.2 Normal probability plot 59

3.6.3 Generating the efficient frontier with Solver 61

Summary 65

References 65

Appendix 3A The Visual Basic Editor 65

Stepping through a macro and using other debug tools 68

Appendix 3B Recording keystrokes in ‘relative references’ mode 69

4 Writing VBA user-defined functions 73

4.1 A simple sales commission function 73

4.2 Creating Commission(Sales) in the spreadsheet 74

4.3 Two functions with multiple inputs for valuing options 75

4.4 Manipulating arrays in VBA 78

4.5 Expected value and variance functions with array inputs 79

4.6 Portfolio variance function with array inputs 81

4.7 Functions with array output 84

4.8 Using Excel and VBA functions in user-defined functions 85

4.8.1 Using VBA functions in user-defined functions 85

4.8.2 Add-ins 86

4.9 Pros and cons of developing VBA functions 86

Summary 87

Appendix 4A Functions illustrating array handling 88

Appendix 4B Binomial tree option valuation functions 89

Exercises on writing functions 94

Solution notes for exercises on functions 95

Part Two Equities 99

5 Introduction to equities 101

6 Portfolio optimisation 103

6.1 Portfolio mean and variance 103

6.2 Risk–return representation of portfolios 105

6.3 Using Solver to find efficient points 106

6.4 Generating the efficient frontier (Huang and Litzenberger’s approach) 109

6.5 Constrained frontier portfolios 111

6.6 Combining risk-free and risky assets 113

6.7 Problem One–combining a risk-free asset with a risky asset 114

6.8 Problem Two–combining two risky assets 115

6.9 Problem Three–combining a risk-free asset with a risky portfolio 117

6.10 User-defined functions in Module1 119

6.11 Functions for the three generic portfolio problems in Module1 120

6.12 Macros in ModuleM 121

Summary 123

References 123

7 Asset pricing 125

7.1 The single-index model 125

7.2 Estimating beta coefficients 126

7.3 The capital asset pricing model 129

7.4 Variance–covariance matrices 130

7.5 Value-at-Risk 131

7.6 Horizon wealth 134

7.7 Moments of related distributions such as normal and lognormal 136

7.8 User-defined functions in Module1 136

Summary 138

References 138

8 Performance measurement and attribution 139

8.1 Conventional performance measurement 140

8.2 Active–passive management 141

8.3 Introduction to style analysis 144

8.4 Simple style analysis 145

8.5 Rolling-period style analysis 146

8.6 Confidence intervals for style weights 148

8.7 User-defined functions in Module1 151

8.8 Macros in ModuleM 151

Summary 152

References 153

Part Three Options on Equities 155

9 Introduction to options on equities 157

9.1 The genesis of the Black–Scholes formula 158

9.2 The Black–Scholes formula 158

9.3 Hedge portfolios 159

9.4 Risk-neutral valuation 161

9.5 A simple one-step binomial tree with risk-neutral valuation 162

9.6 Put–call parity 163

9.7 Dividends 163

9.8 American features 164

9.9 Numerical methods 164

9.10 Volatility and non-normal share returns 165

Summary 165

References 166

10 Binomial trees 167

10.1 Introduction to binomial trees 167

10.2 A simplified binomial tree 168

10.3 The Jarrow and Rudd binomial tree 170

10.4 The Cox, Ross and Rubinstein tree 173

10.5 Binomial approximations and Black–Scholes formula 175

10.6 Convergence of CRR binomial trees 176

10.7 The Leisen and Reimer tree 177

10.8 Comparison of CRR and LR trees 178

10.9 American options and the CRR American tree 180

10.10 User-defined functions in Module0 and Module1 182

Summary 183

References 184

11 The Black–Scholes formula 185

11.1 The Black–Scholes formula 185

11.2 Black–Scholes formula in the spreadsheet 186

11.3 Options on currencies and commodities 187

11.4 Calculating the option’s ‘greek’ parameters 189

11.5 Hedge portfolios 190

11.6 Formal derivation of the Black–Scholes formula 192

11.7 User-defined functions in Module1 194

Summary 195

References 196

12 Other numerical methods for European options 197

12.1 Introduction to Monte Carlo simulation 197

12.2 Simulation with antithetic variables 199

12.3 Simulation with quasi-random sampling 200

12.4 Comparing simulation methods 202

12.5 Calculating greeks in Monte Carlo simulation 203

12.6 Numerical integration 203

12.7 User-defined functions in Module1 205

Summary 207

References 207

13 Non-normal distributions and implied volatility 209

13.1 Black–Scholes using alternative distributional assumptions 209

13.2 Implied volatility 211

13.3 Adapting for skewness and kurtosis 212

13.4 The volatility smile 215

13.5 User-defined functions in Module1 217

Summary 219

References 220

Part Four Options on Bonds 221

14 Introduction to valuing options on bonds 223

14.1 The term structure of interest rates 224

14.2 Cash flows for coupon bonds and yield to maturity 225

14.3 Binomial trees 226

14.4 Black’s bond option valuation formula 227

14.5 Duration and convexity 228

14.6 Notation 230

Summary 230

References 230

15 Interest rate models 231

15.1 Vasicek’s term structure model 231

15.2 Valuing European options on zero-coupon bonds, Vasicek’s model 234

15.3 Valuing European options on coupon bonds, Vasicek’s model 235

15.4 CIR term structure model 236

15.5 Valuing European options on zero-coupon bonds, CIR model 237

15.6 Valuing European options on coupon bonds, CIR model 238

15.7 User-defined functions in Module1 239

Summary 240

References 241

16 Matching the term structure 243

16.1 Trees with lognormally distributed interest rates 243

16.2 Trees with normal interest rates 246

16.3 The Black, Derman and Toy tree 247

16.4 Valuing bond options using BDT trees 248

16.5 User-defined functions in Module1 250

Summary 252

References 252

Appendix Other VBA functions 253

Forecasting 253

ARIMA modelling 254

Splines 256

Eigenvalues and eigenvectors 257

References 258

Index 259