A new, more accurate take on the classical approach to volatility evaluation Inside Volatility Filtering presents a new approach to volatility estimation, using financial econometrics based on a more accurate estimation of the hidden state. Based on the idea of "filtering", this book lays out a two-step framework involving a Chapman-Kolmogorov prior distribution followed by Bayesian posterior distribution to develop a robust estimation based on all available information. This new second edition includes guidance toward basing estimations on historic option prices instead of stocks, as well as Wiener Chaos Expansions and other spectral approaches. The author's statistical trading strategy has been expanded with more in-depth discussion, and the companion website offers new topical insight, additional models, and extra charts that delve into the profitability of applied model calibration. You'll find a more precise approach to the classical time series and financial econometrics evaluation, with expert advice on turning data into profit.
Financial markets do not always behave according to a normal bell curve. Skewness creates uncertainty and surprises, and tarnishes trading performance, but it's not going away. This book shows traders how to work with skewness: how to predict it, estimate its impact, and determine whether the data is presenting a warning to stay away or an opportunity for profit.
- Base volatility estimations on more accurate data
- Integrate past observation with Bayesian probability
- Exploit posterior distribution of the hidden state for optimal estimation
- Boost trade profitability by utilizing "skewness" opportunities
Wall Street is constantly searching for volatility assessment methods that will make their models more accurate, but precise handling of skewness is the key to true accuracy. Inside Volatility Filtering shows you a better way to approach non-normal distributions for more accurate volatility estimation.
Table of Contents:
Foreword ix Acknowledgments (Second Edition) xi
Acknowledgments (First Edition) xiii
Introduction (Second Edition) xv
Introduction (First Edition) xvii
Summary xvii
Contributions and Further Research xxiii
Data and Programs xxiv
CHAPTER 1 The Volatility Problem 1
Introduction 1
The Stock Market 2
The Stock Price Process 2
Historic Volatility 3
The Derivatives Market 5
The Black-Scholes Approach 5
The Cox Ross Rubinstein Approach 7
Jump Diffusion and Level-Dependent Volatility 8
Jump Diffusion 8
Level-Dependent Volatility 11
Local Volatility 14
The Dupire Approach 14
The Derman Kani Approach 17
Stability Issues 18
Calibration Frequency 19
Stochastic Volatility 21
Stochastic Volatility Processes 21
GARCH and Diffusion Limits 22
The Pricing PDE under Stochastic Volatility 26
The Market Price of Volatility Risk 26
The Two-Factor PDE 27
The Generalized Fourier Transform 28
The Transform Technique 28
Special Cases 30
The Mixing Solution 32
The Romano Touzi Approach 32
A One-Factor Monte-Carlo Technique 34
The Long-Term Asymptotic Case 35
The Deterministic Case 35
The Stochastic Case 37
A Series Expansion on Volatility-of-Volatility 39
Local Volatility Stochastic Volatility Models 42
Stochastic Implied Volatility 43
Joint SPX and VIX Dynamics 45
Pure-Jump Models 47
Variance Gamma 47
Variance Gamma with Stochastic Arrival 51
Variance Gamma with Gamma Arrival Rate 53
CHAPTER 2 The Inference Problem 55
Introduction 55
Using Option Prices 58
Conjugate Gradient (Fletcher-Reeves-Polak-Ribiere) Method 59
Levenberg-Marquardt (LM) Method 59
Direction Set (Powell) Method 61
Numeric Tests 62
The Distribution of the Errors 65
Using Stock Prices 65
The Likelihood Function 65
Filtering 69
The Simple and Extended Kalman Filters 72
The Unscented Kalman Filter 74
Kushner’s Nonlinear Filter 77
Parameter Learning 80
Parameter Estimation via MLE 95
Diagnostics 108
Particle Filtering 111
Comparing Heston with Other Models 133
The Performance of the Inference Tools 141
The Bayesian Approach 158
Using the Characteristic Function 172
Introducing Jumps 174
Pure-Jump Models 184
Recapitulation 201
Model Identification 201
Convergence Issues and Solutions 202
CHAPTER 3 The Consistency Problem 203
Introduction 203
The Consistency Test 206
The Setting 206
The Cross-Sectional Results 206
Time-Series Results 209
Financial Interpretation 210
The “Peso” Theory 214
Background 214
Numeric Results 215
Trading Strategies 216
Skewness Trades 216
Kurtosis Trades 217
Directional Risks 217
An Exact Replication 219
The Mirror Trades 220
An Example of the Skewness Trade 220
Multiple Trades 225
High Volatility-of-Volatility and High Correlation 225
Non-Gaussian Case 230
VGSA 232
A Word of Caution 236
Foreign Exchange, Fixed Income, and Other Markets 237
Foreign Exchange 237
Fixed Income 238
CHAPTER 4 The Quality Problem 241
Introduction 241
An Exact Solution? 241
Nonlinear Filtering 242
Stochastic PDE 243
Wiener Chaos Expansion 244
First-Order WCE 247
Simulations 248
Second-Order WCE 251
Quality of Observations 251
Historic Spot Prices 252
Historic Option Prices 252
Conclusion 262
Bibliography 263
Index 279
About the Author :
ALIREZA JAVAHERI is the head of Equities Quantitative Research Americas at JP Morgan and an adjunct professor of Mathematical Finance at the Courant Institute of New York University, as well as Baruch College. He has worked in the field of derivatives quantitative research since 1994 in a variety of investment banks, including Goldman Sachs and Citigroup.
