Inside Volatility FilteringSecrets of the Skew
Wiley Finance 2. Aufl.
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.
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
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.
This fully updated and revised Second Edition of the Wilmott Award-winning book Inside Volatility Arbitrage demonstrates how to filter data using time series and financial econometrics to discover the best possible estimation of hidden opportunities given all the available information up to that point. All-new content includes estimation from historic option prices, instead of stocks, to gain better observation quality; spectral approaches and Wiener Chaos Expansions; and expanded in-depth examples of the statistical trading strategy. In even greater detail, Javaheri shares in-depth information on the relationship between volatility and the stock and derivatives markets, detailed insights on Brownian motion for stock price returns, and option-pricing techniques such as inversion of the Fourier transform and mixing Monte Carlo. Inside Volatility Filtering also illuminates how to: Effectively use a variety of models, from local volatility and stochastic volatility models to pure-jump models Accurately estimate model parameters using two possible sets of data—options prices and historic stock prices Best apply parametric inference methodologies to assets, and why you should question the consistency of information contained in the options and stock markets Additional models and extra illustrative charts show you how to profit in these scenarios using the nuts and bolts of applied model calibration. Inside Volatility Filtering, Second Edition shows you a better way to approach abnormal distributions for more accurate volatility estimation.
"While e-trading typically starts with cash instruments and vanilla securities, it is inevitable that it will eventually encompass trading activities that lean heavily on quantitative elements such as volatility trading. As a result, the Second Edition of this book serves its intended audience well, providing an up-to-date, comprehensive review of the application of filtering techniques to volatility forecasting. While the title of each chapter is framed as a problem, the contents of each chapter represent our best guess at the answer. Employing the advances that econometricians have made in the past quarter century, the fraction of variance explained is a truly impressive accomplishment." —From the Foreword by Peter Carr, Global Head of Market Modeling, Morgan Stanley; and Executive Director, Masters in Math Finance Program, Courant Institute, New York University The New, More Accurate Take on the Classical Approach to Volatility Evaluation Inside Volatility Filtering, Second Edition presents a new approach to volatility estimation identifying financial econometrics based on a more accurate estimation of the hidden state. Based on the idea of "filtering," this practical guide 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 edition gives you an edge by showing you how to: 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 identifying "skewness" opportunities
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