Leverage Python for expert-level volatility and variance derivative trading Listed Volatility and Variance Derivatives is a comprehensive treatment of all aspects of these increasingly popular derivatives products, and has the distinction of being both the first to cover European volatility and variance products provided by Eurex and the first to offer Python code for implementing comprehensive quantitative analyses of these financial products. For those who want to get started right away, the book is accompanied by a dedicated Web page and a Github repository that includes all the code from the book for easy replication and use, as well as a hosted version of all the code for immediate execution. Python is fast making inroads into financial modelling and derivatives analytics, and recent developments allow Python to be as fast as pure C++ or C while consisting generally of only 10% of the code lines associated with the compiled languages. This complete guide offers rare insight into the use of Python to undertake complex quantitative analyses of listed volatility and variance derivatives. Learn how to use Python for data and financial analysis, and reproduce stylised facts on volatility and variance markets Gain an understanding of the fundamental techniques of modelling volatility and variance and the model-free replication of variance Familiarise yourself with micro structure elements of the markets for listed volatility and variance derivatives Reproduce all results and graphics with IPython/Jupyter Notebooks and Python codes that accompany the book Listed Volatility and Variance Derivatives is the complete guide to Python-based quantitative analysis of these Eurex derivatives products.

Table of Contents:
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