If you’re seeking solutions to advanced and even esoteric problems, Advanced Analytical Models goes beyond theoretical discussions of modeling by facilitating a thorough understanding of concepts and their real-world applications—including the use of embedded functions and algorithms. This reliable resource will equip you with all the tools you need to quantitatively assess risk in a range of areas, whether you are a risk manager, business decision-maker, or investor.

Table of Contents:

Preface xv

Software Applications xvii

PART 1 Modeling Toolkit and Risk Simulator Applications 1

Introduction to the Modeling Toolkit Software 1

Introduction to Risk Simulator 2

Running a Monte Carlo Simulation 6

Using Forecast Charts and Confidence Intervals 16

Correlations and Precision Control 18

Tornado and Sensitivity Tools in Simulation 22

Sensitivity Analysis 29

Distributional Fitting: Single Variable and Multiple Variables 33

Bootstrap Simulation 35

Hypothesis Testing 40

Data Extraction, Saving Simulation Results, and Generating Reports 42

Regression and Forecasting Diagnostic Tool 42

Statistical Analysis Tool 52

Distributional Analysis Tool 54

Portfolio Optimization 56

Optimization with Discrete Integer Variables 70

Forecasting 72

1. Analytics—Central Limit Theorem 79

2. Analytics—Central Limit Theorem—Winning Lottery Numbers 84

3. Analytics—Flaw of Averages 88

4. Analytics—Mathematical Integration Approximation Model 93

5. Analytics—Projectile Motion 96

6. Analytics—Regression Diagnostics 100

7. Analytics—Ships in the Night 109

8. Analytics—Statistical Analysis 111

9. Analytics—Weighting of Ratios 123

10. Credit Analysis—Credit Premium 125

11. Credit Analysis—Credit Default Swaps and Credit Spread Options 127

12. Credit Analysis—Credit Risk Analysis and Effects on Prices 129

13. Credit Analysis—External Debt Ratings and Spread 131

14. Credit Analysis—Internal Credit Risk Rating Model 133

15. Credit Analysis—Profit Cost Analysis of New Credit 135

16. Debt Analysis—Asset-Equity Parity Model 137

17. Debt Analysis—Cox Model on Price and Yield of Risky Debt with Mean-Reverting Rates 138

18. Debt Analysis—Debt Repayment and Amortization 141

19. Debt Analysis—Debt Sensitivity Models 145

20. Debt Analysis—Merton Price of Risky Debt with Stochastic Asset and Interest 147

21. Debt Analysis—Vasicek Debt Option Valuation 149

22. Debt Analysis—Vasicek Price and Yield of Risky Debt 151

23. Decision Analysis—Decision Tree Basics 153

24. Decision Analysis—Decision Tree with EVPI, Minimax, and Bayes’ Theorem 158

25. Decision Analysis—Economic Order Quantity and Inventory Reorder Point 169

26. Decision Analysis—Economic Order Quantity and Optimal Manufacturing 170

27. Decision Analysis—Expected Utility Analysis 172

28. Decision Analysis—Inventory Control 174

29. Decision Analysis—Queuing Models 176

30. Exotic Options—Accruals on Basket of Assets 178

31. Exotic Options—American, Bermudan, and European Options with Sensitivities 180

32. Exotic Options—American Call Option on Foreign Exchange 182

33. Exotic Options—American Call Options on Index Futures 184

34. Exotic Options—American Call Option with Dividends 186

35. Exotic Options—Asian Lookback Options Using Arithmetic Averages 188

36. Exotic Options—Asian Lookback Options Using Geometric Averages 189

37. Exotic Options—Asset or Nothing Options 190

38. Exotic Options—Barrier Options 191

39. Exotic Options—Binary Digital Options 193

40. Exotic Options—Cash or Nothing Options 195

41. Exotic Options—Chooser Option (Simple Chooser) 196

42. Exotic Options—Chooser Option (Complex Chooser) 197

43. Exotic Options—Commodity Options 198

44. Exotic Options—Currency (Foreign Exchange) Options 199

45. Exotic Options—Double Barrier Options 200

46. Exotic Options—European Call Option with Dividends 201

47. Exotic Options—Exchange Assets Option 203

48. Exotic Options—Extreme Spreads Option 204

49. Exotic Options—Foreign Equity–Linked Foreign Exchange Options in Domestic Currency 205

50. Exotic Options—Foreign Equity Struck in Domestic Currency 207

51. Exotic Options—Foreign Equity with Fixed Exchange Rate 208

52. Exotic Options—Foreign Takeover Options 209

53. Exotic Options—Forward Start Options 210

54. Exotic Options—Futures and Forward Options 211

55. Exotic Options—Gap Options 212

56. Exotic Options—Graduated Barrier Options 213

57. Exotic Options—Index Options 214

58. Exotic Options—Inverse Gamma Out-of-the-Money Options 215

59. Exotic Options—Jump-Diffusion Options 216

60. Exotic Options—Leptokurtic and Skewed Options 217

61. Exotic Options—Lookback with Fixed Strike (Partial Time) 218

62. Exotic Options—Lookback with Fixed Strike 219

63. Exotic Options—Lookback with Floating Strike (Partial Time) 220

64. Exotic Options—Lookback with Floating Strike 221

65. Exotic Options—Min and Max of Two Assets 222

66. Exotic Options—Options on Options 223

67. Exotic Options—Option Collar 224

68. Exotic Options—Perpetual Options 225

69. Exotic Options—Range Accruals (Fairway Options) 226

70. Exotic Options—Simple Chooser 228

71. Exotic Options—Spread on Futures 229

72. Exotic Options—Supershare Options 230

73. Exotic Options—Time Switch Options 231

74. Exotic Options—Trading-Day Corrections 232

75. Exotic Options—Two-Asset Barrier Options 233

76. Exotic Options—Two Asset Cash or Nothing 234

77. Exotic Options—Two Correlated Assets Option 235

78. Exotic Options—Uneven Dividend Payments Option 237

79. Exotic Options—Writer Extendible Option 238

80. Forecasting—Data Diagnostics 239

81. Forecasting—Econometric, Correlations, and Multiple Regression Modeling 248

82. Forecasting—Exponential J-Growth Curves 254

83. Forecasting—Forecasting Manual Computations 257

84. Forecasting—Linear Interpolation and Nonlinear Spline Extrapolation 259

85. Forecasting—Logistic S-Growth Curves 264

86. Forecasting—Markov Chains and Market Share 267

87. Forecasting—Multiple Regression 269

88. Forecasting—Nonlinear Extrapolation and Forecasting 271

89. Forecasting—Stochastic Processes, Brownian Motion, Forecast Distribution at Horizon, Jump-Diffusion, and Mean-Reversion 273

90. Forecasting—Time-Series ARIMA 276

91. Forecasting—Time-Series Analysis 283

92. Industry Applications—Biotech Manufacturing Strategy 287

93. Industry Applications—Biotech Inlicensing Drug Deal Structuring 289

94. Industry Applications—Biotech Investment Valuation 291

95. Industry Application—Banking: Integrated Risk Management, Probability of Default, Economic Capital,
Value at Risk, and Optimal Bank Portfolios 293

96. Industry Application—Electric/Utility: Optimal Power Contract Portfolios 321

97. Industry Application—IT—Information Security Intrusion Risk Management 329

98. Industry Applications—Insurance ALM Model 349

99. Operational Risk—Queuing Models at Bank Branches 354

100. Optimization—Continuous Portfolio Allocation 356

101. Optimization—Discrete Project Selection 362

102. Optimization—Inventory Optimization 366

103. Optimization—Investment Portfolio Allocation 372

104. Optimization—Investment Capital Allocation I (Basic Model) 373

105. Optimization—Investment Capital Allocation II (Advanced Model) 376

106. Optimization—Military Portfolio and Efficient Frontier 380

107. Optimization—Optimal Pricing with Elasticity 386

108. Optimization—Optimization of a Harvest Model 390

109. Optimization—Optimizing Ordinary Least Squares 394

110. Optimization—Stochastic Portfolio Allocation 400

111. Options Analysis—Binary Digital Instruments 405

112. Options Analysis—Inverse Floater Bond 407

113. Options Analysis—Options-Trading Strategies 413

114. Options Analysis—Options-Adjusted Spreads Lattice 420

115. Options Analysis—Options on Debt 422

116. Options Analysis—Five Plain Vanilla Options 424

117. Probability of Default—Bond Yields and Spreads (Market Comparable) 432

118. Probability of Default—Empirical Model 434

119. Probability of Default—External Options Model (Public Company) 437

120. Probability of Default—Merton Internal Options Model (Private Company) 441

121. Probability of Default—Merton Market Options Model (Industry Comparable) 442

122. Project Management—Cost Estimation Model 443

123. Project Management—Critical Path Analysis (CPM PERT GANTT) 446

124. Project Management—Project Timing 453

125. Real Estate—Commercial Real Estate ROI 456

126. Risk Analysis—Integrated Risk Analysis 460

127. Risk Analysis—Interest Rate Risk 472

128. Risk Analysis—Portfolio Risk Return Profiles 474

129. Risk Hedging—Delta-Gamma Hedging 477

130. Risk Hedging—Delta Hedging 478

131. Risk Hedging—Effects of Fixed versus Floating Rates 479

132. Risk Hedging—Foreign Exchange Cash Flow Model 481

133. Risk Hedging—Hedging Foreign Exchange Exposure 487

134. Sensitivity—Greeks 491

135. Sensitivity—Tornado and Sensitivity Charts Linear 496

136. Sensitivity—Tornado and Sensitivity Nonlinear 503

137. Simulation—Basic Simulation Model 510

138. Simulation—Best Surgical Team 517

139. Simulation—Correlated Simulation 525

140. Simulation—Correlation Effects on Risk 528

141. Simulation—Data Fitting 531

142. Simulation—Debt Repayment and Amortization 534

143. Simulation—Demand Curve and Elasticity Estimation 538

144. Simulation—Discounted Cash Flow, Return on Investment, and Volatility Estimates 542

145. Simulation—Infectious Diseases 546

146. Simulation—Recruitment Budget (Negative Binomial and Multidimensional Simulation) 548

147. Simulation—Retirement Funding with VBA Macros 556

148. Simulation—Roulette Wheel 560

149. Simulation—Time Value of Money 562

150. Six Sigma—Obtaining Statistical Probabilities, Basic Hypothesis Tests, Confidence Intervals, and Bootstrapping Statistics 571

151. Six Sigma—One- and Two-Sample Hypothesis Tests Using t-Tests, Z-Tests, F-Tests, ANOVA, and Nonparametric Tests (Friedman, Kruskal Wallis, Lilliefors, and Runs Tests) 590

152. Six Sigma—Sample Size Determination and Design of Experiments 623

153. Six Sigma—Statistical and Unit Capability Measures, Specification Levels, and Control Charts 627

154. Valuation—Buy versus Lease 631

155. Valuation—Banking: Classified Loan Borrowing Base 634

156. Valuation—Banking: Break-Even Inventory with Seasonal Lending Trial Balance Analysis 637

157. Valuation—Banking: Firm in Financial Distress 640

158. Valuation—Banking: Pricing Loan Fees Model 642

159. Valuation—Valuation Model 644

160. Value at Risk—Optimized and Simulated Portfolio VaR 647

161. Value at Risk—Options Delta Portfolio VaR 651

162. Value at Risk—Portfolio Operational and Credit Risk VaR Capital Adequacy 653

163. Value at Risk—Right-Tail Capital Requirements 657

164. Value at Risk—Static Covariance Method 661

165. Volatility—Implied Volatility 663

166. Volatility—Volatility Computations (Log Returns, Log Assets, Implied Volatility, Management Assumptions, EWMA, GARCH) 664

167. Yield Curve—CIR Model 673

168. Yield Curve—Curve Interpolation BIM Model 674

169. Yield Curve—Curve Interpolation NS Model 676

170. Yield Curve—Forward Rates from Spot Rates 678

171. Yield Curve—Term Structure of Volatility 679

172. Yield Curve—U.S. Treasury Risk-Free Rates and Cubic Spline Curves 680

173. Yield Curve—Vasicek Model 690

PART 2 Real Options SLS Applications 693

174. Introduction to the SLS Software 695

Single Asset and Single Phased Module 697

Multiple Asset or Multiple Phased SLS Module 704

Multinomial SLS Module 705

SLS Excel Solution Module 709

SLS Excel Functions Module 712

Lattice Maker Module 714

175. Employee Stock Options—Simple American Call Option 715

176. Employee Stock Options—Simple Bermudan Call Option with Vesting 716

177. Employee Stock Options—Simple European Call Option 719

178. Employee Stock Options—Suboptimal Exercise 720

179. Employee Stock Options—Vesting, Blackout, Suboptimal, Forfeiture 723

180. Exotic Options—American and European Lower Barrier Options 725

181. Exotic Options—American and European Upper Barrier Options 728

182. Exotic Options—American and European Double Barrier Options and Exotic Barriers 731

183. Exotic Options—Basic American, European, and Bermudan Call Options 734

184. Exotic Options—Basic American, European, and Bermudan Put Options 736

185. Real Options—American, European, Bermudan, and Customized Abandonment Options 739

186. Real Options—American, European, Bermudan, and Customized Contraction Options 749

187. Real Options—American, European, Bermudan, and Customized Expansion Options 756

188. Real Options—Contraction, Expansion, and Abandonment Options 763

189. Real Options—Dual Variable Rainbow Option Using Pentanomial Lattices 767

190. Real Options—Exotic Chooser Options 770

191. Real Options—Exotic Complex Floating American and European Chooser 771

192. Real Options—Jump-Diffusion Option Using Quadranomial Lattices 774

193. Real Options—Mean-Reverting Calls and Puts Using Trinomial Lattices 777

194. Real Options—Multiple Assets Competing Options 779

195. Real Options—Path-Dependent, Path-Independent, Mutually Exclusive, Non–Mutually Exclusive, and
Complex Combinatorial Nested Options 781

196. Real Options—Sequential Compound Options 783

197. Real Options—Simultaneous Compound Options 791

198. Real Options—Simple Calls and Puts Using Trinomial Lattices 795

PART 3 Real Options Strategic Case Studies—Framing the Options 799

199. Real Options Strategic Cases—High-Tech Manufacturing: Build or Buy Decision with Real Options 801

200. Real Options Strategic Cases—Oil and Gas: Farm-Outs, Options to Defer, and Value of Information 810

201. Real Options Strategic Cases—Pharmaceutical Development: Value of Perfect Information and Optimal
Trigger Values 814

202. Real Options Strategic Cases—Option to Switch Inputs 817

203. Valuation—Convertible Warrants with a Vesting Period and Put Protection 821

APPENDIX A List of Models 827

APPENDIX B List of Functions 837

APPENDIX C Understanding and Choosing the Right Probability Distributions 899

APPENDIX D Financial Statement Analysis 919

APPENDIX E Exotic Options Formulae 927

APPENDIX F Measures of Risk 941

APPENDIX G Mathematical Structures of Stochastic Processes 957

Glossary of Input Variables and Parameters in the Modeling Toolkit Software 963

About the DVD 995

About the Author 999

Index 1001