Real Options Valuation (eBook)

Max Schöne is a Ph.D. student at the WHU – Otto Beisheim School of Management with a research focus on real options valuation and decision making under uncertainty.

Foreword 6
Table of contents 7
List of figures 9
List of tables 10
List of abbreviations 11
1 Introduction 13
1.1 Problem and objective 14
1.2 Course of investigation 16
2 Data 18
3 Empirical analysis 21
3.1 Stationarity of prices 21
3.2 Analysis of returns 34
3.2.1 Stylised properties 35
3.2.2 Jumps and GARCH effects 44
4 Modelling commodity prices 52
4.1 Stochastic processes 53
4.1.1 Stochastic volatility 57
4.1.2 Jump diffusion 59
4.1.3 Lévy processes 63
4.2 Model selection 69
4.2.1 Calibration 69
4.2.2 Goodness of fit 74
5 Capital budgeting implications 79
5.1 A stylised investment project 79
5.2 Results 84
6 Conclusion 88
Appendix 90
Appendix A 90
A1: Liquidity of commodity prices. A1: 90
A2: Historical price evolution. A1: 91
A3: Non-trading dates excluded from dataset (1) 92
A3: Non-trading dates excluded from dataset (2) 93
A4: In-sample APDF: Calibrated parameters (1) 94
A4: In-sample APDF: Calibrated parameters (2) 95
A5: Out-of-sample APDF: Calibrated parameters (1) 96
A5: Out-of-sample APDF: Calibrated parameters (2) 97
A6: Capital investment project: Valuation parameters 98
Appendix B 99
B1: Expected value and variance for GBM and the Vasicek model: 99
B2: Maximum likelihood calibration: 99
B3: Characteristic function and Fourier transforms 101
B4: Quadratic exponential scheme for Heston and Bates process 102
B5: Basis functions and confidence intervals in LSM 105
References 107