Inside Volatility Filtering - Secrets of the Skew

Author and financial expert Alireza Javaheri uses the classic approach to evaluating volatility--time series and financial econometrics--in a way that he believes is superior to methods presently used by market participants. He also suggests that there may be "skewness" trading opportunities that can be sued to trade the markets mroe profitably. Filed with in-depth insight and expert advice, this book will focus on the idea of filtering.
The idea behind filtering is to obtain the best possible estimation of a hidden state given all the available information up to that point. This estimation is done in an iterative manner in two stages: The first step is a time update in which the prior distribution from all the past information via a Chapman-Kolmogorov equation. The second step would then involve a measurement update where this prior distribution is used together with the conditional likelihood of the newest observation in order to compute the posterior distribution of the hidden state. The Bayes rule is used for this purpose. Once the posterior distribution is determined, it can be exploited for the optimal estimation of the hidden state.
For practitioners and students, the author is adding content on:
* estimation from historic option prices instead of stocks, as the observation quality is better
* spectral approaches and in particular Wiener Chaos Expansions
* on the statistical trading strategy in section 3

List 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<

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.

Summary

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.

Product details

• Authors: a Javaheri, Alireza Javaheri, Javaheri Alireza
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 09.10.2015
• EAN: 9781118943977
• ISBN: 978-1-118-94397-7
• No. of pages: 320
• Series: Wiley Finance; Wiley Finance Editions; The Wiley Finance Series; Wiley Finance; Wiley Finance Editions
• Subjects: Social sciences, law, business > Business > Business administration; trading, Börsenhandel, Finance & Investments, Finanz- u. Anlagewesen