Systematic Options Trading Evaluating, Analyzing, and Profiting from Mispriced Option Opportunities

Sergey Izraylevich, Ph.D., chairman of the board of High Technology Invest Inc., began his career as a lecturer at The Hebrew University of Jerusalem and Tel-Hay Academic College. He received numerous awards for academic excellence, including Golda Meir’s prize and the Max Shlomiok honor award of distinction. Sergey has traded options for more than 10 years and engages in creating automated systems for the algorithmic trading of options. He is the author of numerous articles published in highly rated, peer-reviewed scientific journals. Sergey is a columnist for Futures magazine.

Vadim Tsudikman, president of High Technology Invest Inc., is a financial consultant and investment advisor specializing in derivatives valuation, hedging, and capital allocation in extreme market environments. With 12 years of options trading experience, he develops complex trading systems based on multicriteria analyses and genetic optimization algorithms. In co-authorship with Sergey Izraylevich, Vadim contributes articles to Futures magazine on the cutting-edge issues related to options pricing, volatility, and risk management.

Introduction xv

PART I Criteria as the Basis of a Systematic Approach

chapter 1 General Presentation and Review of Criteria Properties 3

1.1 The Main Tool for Solving the Selection Problem 3

1.2 Formal Definition 4

1.3 Philosophy of Criteria Creation 5

1.4 Mission Fulfilled by Criteria 6

1.5 Forecast as a Key Element of the Criterion 8

1.6 Classification of Criteria 9

1.6.1 Universal Criteria 9

1.6.2 Specific (Nonuniversal) Criteria 11

chapter 2 Review of the Main Criteria 13

2.1 Criteria Based on Lognormal Distribution 13

2.1.1 Description of Lognormal Distribution 13

2.1.2 Expected Profit on the Basis of Lognormal Distribution 15

2.1.3 Profit Probability on the Basis of Lognormal Distribution 20

2.2 Criteria Based on Empirical Distribution 22

2.2.1 Description of Empirical Distribution 22

2.2.2 Expected Profit on the Basis of Empirical Distribution 25

2.2.3 Profit Probability on the Basis of Empirical Distribution 28

2.2.4 Simplified Calculation Algorithm 28

2.2.5 Modifications of Empirical Distribution 31

2.3 Criteria Based on the Ratio of Expected Profit to Loss 34

2.3.1 Basic Concept and Criteria Calculation Method 34

2.3.2 Criteria Calculation Example 36

2.4 Criteria Based on Expert Distribution 38

2.4.1 Basic Concept and Criteria Calculation Method 38

2.4.2 Set of Standard Distributions 39

2.4.3 Combining Separate Standard Distributions into a Unified Probability Density Function 45

2.4.4 Criteria Calculation on the Basis of the Unified Probability Density Function 47

2.4.5 Construction and Valuation of Complex Strategies Based on the Unified Probability Density Function 48

2.5 Specific (Nonuniversal) Criteria 50

2.5.1 Break-Even Range 50

2.5.2 IV/HV Ratio 53

2.5.3 Relative Frequency Criterion 57

2.5.4 The Ratio of Normalized Time Value to the Coefficient of Absolute Price Changes Distribution 58

chapter 3 Evaluation of Criteria Effectiveness 63

3.1 Introduction 63

3.2 Methods of Criteria Effectiveness Evaluation 64

3.2.1 Correlation Between a Criterion and Profit as the Main Effectiveness Indicator 64

3.2.2 Transformation of the Criteria Effectiveness Indicator 68

3.2.3 The Dynamics of Transformed Effectiveness Indicators 69

3.2.4. Selection of the Averaging Period 72

3.3 Peculiarities of Criteria Effectiveness Evaluation 75

3.3.1 Number of Combinations Used in the Analysis 75

3.3.2 Expressing Profit 77

3.3.3 Expressing Effectiveness Indicators 80

3.4 Review of Criteria Effectiveness Indicators 84

3.4.1 Correlation Between Criterion and Profit Values 85

3.4.2 Correlation Between a Criterion and Profit Indexes 86

3.4.3 Correlation Between the Sharpe Ratios of Criterion and Profit 88

3.4.4 Areas Ratio 91

3.4.5 Other Effectiveness Indicators 96

3.5 Summary 102

PART II The Main Areas of Criteria Application

chapter 4 Selection of Option Combinations 105

4.1 Introduction 105

4.2 Analysis of Criteria Effectiveness in the Selection of Option Combinations 106

4.3 Factors That Affect Option Combinations Selection 110

4.3.1 Absolute Values of the Criterion 110

4.3.2 Strategy and Underlying Assets 112

4.3.3 Simultaneous Analysis of Factors Affecting Combinations Selection 113

4.4 Multistrategy, Long-Term Evaluation of Criteria Effectiveness 115

4.4.1 Methods 115

4.4.2 Results 116

4.5 Summary 119

chapter 5 Selection of Option Strategies 121

5.1 Introduction 121

5.2 Evaluation of Criterion Effectiveness by Ranking Analysis 123

5.2.1 Methods of Ranking Analysis 123

5.2.2 Results of Ranking Analysis 131

5.2.3 Generalized Ranking Analysis and Introduction of the Threshold Parameter 139

5.2.4 Results of Generalized Ranking Analysis 140

5.2.5 Maximum Obtainable Values of the Criterion Effectiveness Coefficient 142

5.3 Traditional Methods of Evaluating the Criterion Effectiveness 145

5.4 Synthetic Approach to Criterion Effectiveness Analysis 150

5.5 The Model for Optimizing the Threshold Parameter 155

5.6 Summary 159

chapter 6 Selection of Underlying Assets 161

6.1 Introduction 161

6.2 Analysis of Criteria Effectiveness in Selection of Underlying Assets 162

6.3 Multistrategy, Long-Term Evaluation of Criteria Effectiveness 166

6.3.1 Methods 166

6.3.2 Results 167

6.4 The Optimization Model for the Number of Underlying Assets 168

6.4.1 Utility Indicators 169

6.4.2 Utility Functions 171

6.4.3 Convolution of Utility Functions and Deriving

Optima for Different Strategies and Criteria 173

6.5 Summary 176

PART III Multicriteria Analysis

chapter 7 Basic Concepts of Multicriteria Selection as Applied to Options 181

7.1 Introduction 181

7.2 The Pareto Set 183

7.2.1 The Algorithm of Forming the Pareto Set 183

7.2.2 Widening the Pareto Set and the “Layer” Notion 186

7.3 Convolution 190

7.4 Comparative Analysis of Multicriteria and Monocriterion Selection Effectiveness 191

7.5 Comparative Analysis of Two Multicriteria Selection Methods: Pareto Versus Convolution 197

7.6 Summary 202

chapter 8 The Impact of Criteria Correlation on Multicriteria

Selection 205

8.1 Introduction 205

8.2 Evaluation of Criteria Interrelationship 206

8.3 Criteria Correlation and Profitability of Pareto Selection 208

8.4 Criteria Correlation and Profitability of Selection Using the Convolution Method 212

8.5 Summary 214

Conclusion 217

Bibliography 219

appendix Basic Notions 223

Index 235

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