Listed Volatility and Variance Derivatives: A Python-based Guide

Content: Preface xi     PART ONE Introduction to Volatility and Variance     CHAPTER 1 Derivatives, Volatility and Variance 3     1.1 Option Pricing and Hedging 3     1.2 Notions of Volatility and Variance 6     1.3 Listed Volatility and Variance Derivatives 7     1.3.1 The US History 7     1.3.2 The European History 8     1.3.3 Volatility of Volatility Indexes 9     1.3.4 Products Covered in this Book 10     1.4 Volatility and Variance Trading 11     1.4.1 Volatility Trading 11     1.4.2 Variance Trading 13     1.5 Python as Our Tool of Choice 14     1.6 Quick Guide Through the Rest of the Book 14     CHAPTER 2 Introduction to Python 17     2.1 Python Basics 17     2.1.1 Data Types 17     2.1.2 Data Structures 20     2.1.3 Control Structures 22     2.1.4 Special Python Idioms 23     2.2 NumPy 28     2.3 matplotlib 34     2.4 pandas 38     2.4.1 pandas DataFrame class 39     2.4.2 Input-Output Operations 45     2.4.3 Financial Analytics Examples 47     2.5 Conclusions 53     CHAPTER 3 Model-Free Replication of Variance 55     3.1 Introduction 55     3.2 Spanning with Options 56     3.3 Log Contracts 57     3.4 Static Replication of Realized Variance and Variance Swaps 57     3.5 Constant Dollar Gamma Derivatives and Portfolios 58     3.6 Practical Replication of Realized Variance 59     3.7 VSTOXX as Volatility Index 65     3.8 Conclusions 67     PART TWO Listed Volatility Derivatives     CHAPTER 4 Data Analysis and Strategies 71     4.1 Introduction 71     4.2 Retrieving Base Data 71     4.2.1 EURO STOXX 50 Data 71     4.2.2 VSTOXX Data 74     4.2.3 Combining the Data Sets 76     4.2.4 Saving the Data 78     4.3 Basic Data Analysis 78     4.4 Correlation Analysis 83     4.5 Constant Proportion Investment Strategies 87     4.6 Conclusions 93     CHAPTER 5 VSTOXX Index 95     5.1 Introduction 95     5.2 Collecting Option Data 95     5.3 Calculating the Sub-Indexes 105     5.3.1 The Algorithm 106     5.4 Calculating the VSTOXX Index 114     5.5 Conclusions 118     5.6 Python Scripts 118     5.6.1 index collect option-data.py 118     5.6.2 index-subindex-calculation.py 123     5.6.3 index-vstoxx-calculation.py 127     CHAPTER 6 Valuing Volatility Derivatives 129     6.1 Introduction 129     6.2 The Valuation Framework 129     6.3 The Futures Pricing Formula 130     6.4 The Option Pricing Formula 132     6.5 Monte Carlo Simulation 135     6.6 Automated Monte Carlo Tests 141     6.6.1 The Automated Testing 141     6.6.2 The Storage Functions 145     6.6.3 The Results 146     6.7 Model Calibration 153     6.7.1 The Option Quotes 154     6.7.2 The Calibration Procedure 155     6.7.3 The Calibration Results 160     6.8 Conclusions 163     6.9 Python Scripts 163     6.9.1 srd-functions.py 163     6.9.2 srd simulation analysis.py 167     6.9.3 srd simulation results.py 171     6.9.4 srd model calibration.py 174     CHAPTER 7 Advanced Modeling of the VSTOXX Index 179     7.1 Introduction 179     7.2 Market Quotes for Call Options 179     7.3 The SRJD Model 182     7.4 Term Structure Calibration 183     7.4.1 Futures Term Structure 184     7.4.2 Shifted Volatility Process 190     7.5 Option Valuation by Monte Carlo Simulation 191     7.5.1 Monte Carlo Valuation 191     7.5.2 Technical Implementation 192     7.6 Model Calibration 195     7.6.1 The Python Code 196     7.6.2 Short Maturity 199     7.6.3 Two Maturities 201     7.6.4 Four Maturities 203     7.6.5 All Maturities 205     7.7 Conclusions 209     7.8 Python Scripts 210     7.8.1 srjd fwd calibration.py 210     7.8.2 srjd-simulation.py 212     7.8.3 srjd-model-calibration.py 215     CHAPTER 8 Terms of the VSTOXX and its Derivatives 221     8.1 The EURO STOXX 50 Index 221     8.2 The VSTOXX Index 221     8.3 VSTOXX Futures Contracts 223     8.4 VSTOXX Options Contracts 224     8.5 Conclusions 225     PART THREE Listed Variance Derivatives     CHAPTER 9 Realized Variance and Variance Swaps 229     9.1 Introduction 229     9.2 Realized Variance 229     9.3 Variance Swaps 235     9.3.1 Definition of a Variance Swap 235     9.3.2 Numerical Example 235     9.3.3 Mark-to-Market 239     9.3.4 Vega Sensitivity 241     9.3.5 Variance Swap on the EURO STOXX 50 242     9.4 Variance vs. Volatility 247     9.4.1 Squared Variations 247     9.4.2 Additivity in Time 247     9.4.3 Static Hedges 250     9.4.4 Broad Measure of Risk 250     9.5 Conclusions 250     CHAPTER 10 Variance Futures at Eurex 251     10.1 Introduction 251     10.2 Variance Futures Concepts 252     10.2.1 Realized Variance 252     10.2.2 Net Present Value Concepts 252     10.2.3 Traded Variance Strike 257     10.2.4 Traded Futures Price 257     10.2.5 Number of Futures 258     10.2.6 Par Variance Strike 258     10.2.7 Futures Settlement Price 258     10.3 Example Calculation for a Variance Future 258     10.4 Comparison of Variance Swap and Future 265     10.5 Conclusions 268     CHAPTER 11 Trading and Settlement 269     11.1 Introduction 269     11.2 Overview of Variance Futures Terms 269     11.3 Intraday Trading 270     11.4 Trade Matching 274     11.5 Different Traded Volatilities 275     11.6 After the Trade Matching 277     11.7 Further Details 279     11.7.1 Interest Rate Calculation 279     11.7.2 Market Disruption Events 280     11.8 Conclusions 280     PART FOUR DX Analytics     CHAPTER 12 DX Analytics     An Overview 283     12.1 Introduction 283     12.2 Modeling Risk Factors 284     12.3 Modeling Derivatives 287     12.4 Derivatives Portfolios 290     12.4.1 Modeling Portfolios 292     12.4.2 Simulation and Valuation 293     12.4.3 Risk Reports 294     12.5 Conclusions 296     CHAPTER 13 DX Analytics     Square-Root Diffusion 297     13.1 Introduction 297     13.2 Data Import and Selection 297     13.3 Modeling the VSTOXX Options 301     13.4 Calibration of the VSTOXX Model 303     13.5 Conclusions 308     13.6 Python Scripts 308     13.6.1 dx srd calibration.py 308     CHAPTER 14 DX Analytics     Square-Root Jump Diffusion 315     14.1 Introduction 315     14.2 Modeling the VSTOXX Options 315     14.3 Calibration of the VSTOXX Model 320     14.4 Calibration Results 325     14.4.1 Calibration to One Maturity 325     14.4.2 Calibration to Two Maturities 325     14.4.3 Calibration to Five Maturities 325     14.4.4 Calibration without Penalties 331     14.5 Conclusions 332     14.6 Python Scripts 334     14.6.1 dx srjd calibration.py 334     Bibliography 345     Index 347