Stochastic Dominance Option Pricing (eBook)

Dedication 5
Foreword 6
Preface 8
References 12
Contents 14
List of Figures 15
List of Tables 19
Chapter 1: Stochastic Dominance: Introduction 22
1.1 Definition 23
1.2 Risk and Second-Degree Stochastic Dominance 26
1.3 Empirical Applications and Portfolio Selection Under SSD or TSD 31
1.4 Empirical Tests of Stochastic Dominance 33
1.5 Summary and Conclusions 36
References 37
Chapter 2: Stochastic Dominance Option Pricing I: The Frictionless Case 39
2.1 SD Option Pricing by Pairwise Comparisons 40
2.2 SD Option Pricing: The Linear Programming Approach 50
2.3 The Frictionless SD Bounds in Continuous Time for Diffusion 56
Index Options 58
Equity Options 60
2.4 The Frictionless SD Bounds in Continuous Time for Jump Diffusion I: Index Options 65
Upper and Lower Bound for Jump Diffusion 66
Numerical Results 74
Stochastic Dominance and Equilibrium Option Prices 77
2.5 The Frictionless SD Bounds in Continuous Time for Jump Diffusion II: Equity Options 82
2.6 An Important Application of Jump Diffusion: Catastrophe (CAT) Derivatives 88
The Valuation Model for Convex Payoffs Without a CAT Futures Market 90
Claims with Non-Convex Payoffs but with a CAT Futures Market 93
Catastrophe (CAT) Bonds and Reinsurance Contracts 97
2.7 Summary and Conclusions 99
References 102
Chapter 3: Proportional Transaction Costs: An Introduction 106
3.1 No Arbitrage Under Transaction Costs 109
Replicating Portfolios 110
Super Replication and the Failure of No Arbitrage 114
3.2 Portfolio Selection Under Proportional Transaction Costs 116
Asset Allocation in Discrete Time 116
The No Trade Region in Continuous Time for an Infinite Investment Horizon 118
What Happens When the Horizon Is Finite? 121
3.3 Simultaneous Equilibrium in the Underlying and Option Markets 122
3.4 Summary and Conclusions 126
References 127
Chapter 4: Stochastic Dominance Option Pricing II: Option Bounds Under Transaction Costs 129
4.1 European Index Option Bounds Under Transaction Costs 131
The Upper Bound of a European Call Option and the Lower Bound of a European Put Option 133
The Lower Bound of a European Call Option 140
4.2 American Index Option Bounds Under Transaction Costs 153
The Upper Bound of an American Index Call Option 154
The Lower Bound of an American Index Put Option 158
Bounds on the Prices of American Index Futures Options as in Theorems 5 and 6 162
The Lower Bound of an American Call Index and Index Futures Option 165
4.3 Summary and Conclusions 168
4.4 Mathematical Appendix 170
Proof of Lemma 1 170
Proof of Theorem 3 172
Proof of Theorem 4 178
Proof of Lemma 2 181
Proof of Theorem 5 182
Proof of Theorem 6 188
References 192
Chapter 5: Stochastic Dominance Option Pricing: Empirical Applications 194
5.1 Empirical Applications I: Pricing the Option Cross-Section Under Transaction Costs 196
5.2 Empirical Applications II: Individually Mispriced Options Under Transaction Costs 199
In-Sample Tests on Individual Options’ Mispricing 199
Out-of-Sample Tests of Individual Options’ Mispricing 200
5.3 Empirical Applications III: Mispriced Option Portfolios Under Transaction Costs 208
5.4 Mispriced Option Portfolios in the Frictionless Economy 215
Does a U-Shaped Pricing Kernel Explain the Anomalous OT Results? 217
The U-Shaped Kernel, the OT Portfolios and the “Anomalous” Straddles and Puts 220
5.5 Conclusions 222
References 223
Chapter 6: Stochastic Dominance and Further Theoretical and Empirical Option Research 226
6.1 Stochastic Dominance, Stochastic Volatility and GARCH 228
Stochastic Volatility 229
GARCH Asset Dynamics 234
6.2 Stochastic Dominance and Empirical Option Anomalies 240
The U-Shaped Pricing Kernel Under Frictions: Implications for Further Research 240
Are Put Options Expensive? 243
6.3 Bid-Ask Spreads in the Option Market 249
Modeling the Supply: The Market Maker’s Option Bid and Ask Quotes 250
Modeling Demand and Market Equilibrium 256
6.4 Alternative Investor Preferences and Option Pricing 259
The Epstein-Zin (1989) Recursive Utility 259
Stochastic Dominance, Prospect Theory and Option Pricing 260
6.5 Conclusions 264
References 265
Chapter 7: Conclusions 270
References 276
Bibliography 278
Index 288