Handbook of Recent Advances in Commodity and Financial Modeling (eBook)

Giorgio Consigli is an Associate Professor, Department of Management, Economics and Quantitative Methods at the University of Bergamo, Italy. His research interests include stochastic modeling of financial and commodity markets, applied stochastic optimization to long term financial planning problems, approximation methods for large scale optimization and financial engineering applications. He has been Member of the International Commission on Stochastic Programming (COSP) from 2007 to 2013 and since 2014 he is Coordinator of the EURO working Group on Stochastic Optimization. He received his undergraduate degree in Economics (Honors) at the University of Rome, La Sapienza, where he also earned his MS in Banking, and earned his Ph.D. in Mathematics at Cambridge University, where he was supervised by M.A.H. Dempster. He is a Springer author.Silvana Stefani has been a Full Professor of Mathematics Applied to Economics and Finance at the University of Milan, Bicocca, since 2000. Her main research activities are in Discrete Mathematics applied to economics and finance; Stochastic Processes applied to finance and energy series; Energy and environmental markets; and Ranking and journal classification using fuzzy statistical techniques. She has published several books in both English and Italian (one with Springer).  Giovanni Zambruno is a Full Professor at the University of Milan, Bicocca, Department of Statistics and Quantitative Methods. His research interests are Financial Mathematics, Applied Calculus, and Economics. He has been President of the Faculty Council of the MSc program in Economics and Finance since 2002, and was Coordinator of the Doctoral program in Mathematical Finance from 2005-2013.

Preface 5
Contents 12
Part I Risk Modeling 14
1 Directional Returns for Gold and Silver: A Cluster Analysis Approach 15
1.1 Introduction and Literature Review 15
1.2 Data Collection and Preparation 16
1.3 Methodology: Two-Step Cluster Analysis 19
1.4 Gold with Clusters 22
1.4.1 Training Set Variable Importance 22
1.4.2 Validation Set Results for the Gold Models 24
1.5 Silver with Clusters 25
1.5.1 Training Set Variable Importance 25
1.5.2 Validation Set Results for the Silver Models 26
1.6 Summary and Conclusions 27
References 28
2 Impact of Credit Risk and Business Cycles on Momentum Returns 29
2.1 Introduction 30
2.2 Literature Review 32
2.2.1 The Persistence of Momentum Returns in Different Dimensions 32
2.2.2 Momentum Returns and Credit Ratings 32
2.2.3 Momentum Returns and Risk Factors 33
2.3 Data 34
2.3.1 Methods 36
2.4 Empirical Findings 36
2.4.1 Can the Fama-French Three Factors Explain Momentum Returns in Credit-Rated Stocks? 43
2.4.2 Can Market States Explain the Momentum Returns in Credit-Rated Stocks? 43
2.4.3 Can Macroeconomic Factors Explain the Momentum Returns in Credit-Rated Stocks? 46
2.5 Conclusions 48
Appendix: S& P Credit Rating
References 49
3 Drivers of LBO Operating Performance: An Empirical Investigation in Asia 52
3.1 Introduction 52
3.2 Literature Review 55
3.2.1 Tax Benefit 55
3.2.2 Free Cash-Flow 56
3.2.3 Ownership Structure 56
3.2.4 Macroeconomic Factors 57
3.3 Institutional Background of Emerging Economies: The Case of Asia 58
3.3.1 Academic Background 59
3.3.2 Institutional Background 59
3.4 Data Sources and Descriptive Statistics 60
3.4.1 Sample Description 61
3.4.2 Benchmark Comparison 61
3.4.3 Descriptive Statistics 62
3.4.4 Analysis and Discussion 62
3.5 Results 69
3.5.1 OLS Model 70
3.5.2 Introduction of LBO Dummy Variable 70
3.5.3 Introduction of Geographical Area Dummy Variables 72
3.5.4 Geographical Areas and Governance (Table 3.8) 72
3.5.5 Efficiency and Profitability Impacts (Table 3.9) 72
3.6 Conclusion 74
References 76
4 Time Varying Correlation: A Key Indicator in Finance 79
4.1 Introduction 80
4.2 Recent Literature 81
4.3 The Correlation Measure 82
4.3.1 Data Simulation 84
4.3.2 Comparing the Correlation Estimators 86
4.4 Measuring Correlation 89
4.4.1 Stationarity of the Series 89
4.4.2 Structural Breaks 89
4.4.3 Correlations Between Commodities and Financial Markets 91
4.4.4 Correlations Between Energy Commodities 94
4.5 Concluding Remarks 96
References 97
5 Measuring Model Risk in the European Energy Exchange 98
5.1 Introduction and Background 98
5.2 The Relative Measure of Model Risk 101
5.3 Data and Preliminary Analysis 103
5.4 Model Setting and Estimation 105
5.4.1 The GARCH Methodology 106
5.4.2 Dynamic Model Risk Quantification 111
5.5 Empirical Results 112
5.6 Conclusions and Future Research 115
References 118
Part II Pricing and Valuation 120
6 Wine Futures: Pricing and Allocation as Levers Against Quality Uncertainty 121
6.1 Introduction 122
6.1.1 Winemaking Process and the Tasting Reviews 122
6.2 Literature Review 124
6.2.1 Pricing and Quantity Decisions Under Uncertainty 124
6.2.2 Advance Selling 125
6.2.3 Wine Tasting 125
6.2.4 Contribution over Noparumpa et al. (2015a) 126
6.3 The Model 126
6.3.1 The Model 128
6.3.2 Demand for Wine Futures 129
6.4 Analysis 130
6.5 Empirical Analysis with Bordeaux Winery Data 132
6.5.1 Wine Futures as a Quantity Lever 132
6.5.2 Wine Futures as a Price Lever 136
6.5.3 Financial Benefit from the Proposed Stochastic Optimization Model 138
6.5.4 Financial Impact from a Wine Futures Market 140
6.6 Conclusions 143
Appendix 144
References 146
7 VIX Computation Based on Affine Stochastic Volatility Modelsin Discrete Time 148
7.1 Introduction 148
7.2 General Setup 151
7.3 VIX Index 154
7.4 Special Cases 156
7.4.1 Dynamic Variance Gamma 157
7.4.2 Dynamic Normal Inverse Gaussian 158
7.4.3 Dynamic Normal Tempered Stable 159
7.5 Empirical Analysis 160
7.6 Conclusions 164
A Appendix 165
A.1 Conditional Moment Generating Function 165
A.2 Martingale Condition 166
A.3 VIX Index: Derivation Formula 167
A.4 VIX Index: Autoregressive Model 169
References 170
8 Optimal Adaptive Sequential Calibration of Option Models 172
8.1 Introduction 172
8.2 Methods 174
8.2.1 Review of Calibration Methods 174
8.2.2 Extended Parameter Dynamics 177
8.2.2.1 Random Walk Dynamics 177
8.2.2.2 Random Coefficient Dynamics 177
8.2.2.3 Mean Reversion Dynamics 178
8.2.3 Optimal Tuning 178
8.2.4 Model Selection 181
8.3 Simulations 181
8.4 Empirical Study 183
8.4.1 The Black-Scholes Model 184
8.4.2 The Heston Model 184
8.4.2.1 Numerical Results 186
8.5 Conclusion 186
References 187
9 Accurate Pricing of Swaptions via Lower Bound 189
9.1 Introduction 189
9.2 A Lower Bound on Swaption Prices 192
9.2.1 Affine Models 192
9.3 The Geometric Average Approximate Exercise Region 194
9.4 Models and Numerical Results 195
9.4.1 Affine Gaussian Models 195
9.4.2 Multi-factor Cox-Ingersoll-Ross (CIR) Model 196
9.4.3 Gaussian Model with Double Exponential Jumps 197
9.4.4 Balduzzi, Das, Foresi and Sundaram Model 199
9.4.5 Numerical Results 199
9.4.5.1 Vasicek Model, Three-Factors Gaussian Model and Cox-Ingersoll and Ross Model 200
9.4.5.2 Two-Factor Gaussian Model with Double Exponential Jumps 211
9.4.5.3 Balduzzi, Das, Foresi and Sundaram Model 211
9.5 Conclusions 211
A Appendix 212
A.1 Proof Proposition 1 212
A.2 Proof of the Analytical Lower Bound for Gaussian Affine Models 213
References 214
Part III Optimization Techniques 215
10 Portfolio Optimization Using Modified Herfindahl Constraint 216
10.1 Introduction 216
10.2 Review of the Constraints About Diversification 219
10.2.1 Upper-Bound Constraint 219
10.2.2 Lower-Bound Constraint 220
10.2.3 Lp-Norm Constraint 220
10.2.4 Entropy Constraint 221
10.3 Portfolio Allocation Models Under Consideration 222
10.3.1 Risk-Based Strategies 222
10.3.1.1 Equally Weighted Portfolio (EW) 222
10.3.1.2 The Shortsale-Constrained Global Minimum-Variance Portfolio (GMV) 223
10.3.1.3 The Shortsale-Constrained Equal Risk Contribution Portfolio (ERC) 223
10.3.1.4 The Shortsale-Constrained Maximum Diversified Portfolio (MDP) 224
10.3.2 Taylor Approximation of the Expected Utility (EU) with Constraints on Portfolio Diversification 224
10.3.2.1 Diversifying Portfolios Through Weight Constraint 225
10.4 Empirical Analysis 227
10.4.1 Description of the Data Base 227
10.4.2 Empirical Protocol 228
10.4.2.1 In-Sample 229
10.4.2.2 Out-of-Sample 229
10.4.3 Results with MHI-Constraint 230
10.5 Conclusions 232
References 243
11 Dynamic Asset Allocation with Default and Systemic Risks 245
11.1 Introduction 245
11.2 No-Arbitrage Dynamics of the Risky Asset Values 246
11.3 The Optimal Investment Rule 248
11.4 Numerical Analysis 251
11.5 Conclusions 252
References 254
12 Optimal Execution Strategy in Liquidity FrameworkUnder Exponential Temporary Market Impact 255
12.1 Introduction 255
12.2 The Model Framework 257
12.3 Exponential Market Impact Function 261
12.3.1 Evaluation of W-1 264
12.4 Conclusion 265
A Lambert W Function 266
A.1 Taylor Series for -1e< z<
A.2 Series Expansions About the Branch Point z=-1e 267
A.3 Asymptotic Series for z< 0
References 268
13 Optimal Multistage Defined-Benefit Pension Fund Management 270
13.1 Introduction 270
13.2 DB Pension Fund Management 272
13.3 Liabilities, Liquidity and A-L Duration Matching 276
13.4 Risk Capital and Risk-Adjusted Performance 280
13.5 Funding Conditions and ALM Optimization 282
13.6 Case Study: A 20 Year Pension Fund ALM Problem 286
13.6.1 Evolution of Funding Conditions 289
13.6.2 Worst Case Scenario Analysis 293
13.7 Conclusion 295
Appendix 296
References 298
14 Currency Hedging for a Multi-national Firm 300
14.1 Introduction 301
14.2 Exchange Rate Models 302
14.2.1 Review of Exchange Rate Studies 302
14.2.2 An Equilibrium Correction Model 303
14.2.3 Taylor Rule Based Models 304
14.2.4 Random Walk Model 305
14.3 A Dynamic Hedging Model 306
14.3.1 Exchange Rate Scenarios 306
14.3.2 Revenues and Expenditures 307
14.3.3 Forwards and Options 309
14.3.4 Model Formulation 310
14.4 Comparison of Hedging Strategies Over a Single Year 312
14.5 Out-of-Sample Tests 315
14.6 Conclusions 320
Appendix: Hedging Results with Exchange Rate Model EqC and TrE 322
References 323