Financial markets—whether you're dealing with stocks or options—don't always behave according to a normal distribution pattern. Instead, they sometimes exhibit "fat tails," which are defined as prices that are skewed far away from the normal bell curve. If the bulk of returns are pushed to the right, then the distribution has positive skewness. The danger lies in negatively skewed distribution with excess kurtosis, which means there's a high probability of losses much larger than the mean. When dealing with volatility arbitrage, you must take these issues into account in order to manage risk and capture profits.

With Inside Volatility Arbitrage: The Secrets of Skewness, Alireza Javaheri provides one of the most comprehensive looks at this important topic. Divided into three informative sections, this guide focuses on developing methodologies for estimating stochastic volatility (SV) parameters from the stock-price time-series under a classical framework.

In Section 1: The Volatility Problem, Javaheri introduces the concept of various parametric SV models and examines literature on the subject of non-deterministic volatility. Here, you'll receive 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. You'll also gain invaluable knowledge on a variety of models, from local volatility and stochastic volatility models to pure-jump models.

In Section 2: The Inference Problem, Javaheri tackles the notion of inference (or parameter estimation) for parametric SV models—briefly analyzing cross-sectional inference and then focusing on time-series inference. Here you'll discover how to estimate model parameters using two possible sets of data: options prices and historic stock prices.

Finally, in Section 3: The Consistency Problem, Javaheri shows you how to apply parametric inference methodologies to a few assets. He also reveals why you should question the consistency of information contained in the options markets and the stock market.

Filled with in-depth insights, proven models, and illustrative charts, Inside Volatility Arbitrage will help you realize when "skewness" may present valuable trading opportunities, as well as why it can be so profitable.

"...ideal for academics and practitioners who want to focus on volatility modeling. . . All of this makes the book rich and valuable. . . Go and get it!" (Wilmottmagazine, September 2005)

"Best New Quantitative Finance Book of the Year" (Wilmott Awards 2006)

Order your copy of this groundbreaking new work on assessing volatility using financial econometrics to trade against skewness scenarios today.

Praise for INSIDE VOLATILITY ARBITRAGE

"I have been repeatedly asked by students, trainees, and even experienced traders where to learn about volatility surface and the dynamics of stochastic volatility. Until this book, I was at a loss for an answer. This is a wonderful book and a deep, thoughtful, and complete tool."

—Nassim Nicholas Taleb, author of Fooled by Randomness

"To stay competitive you must have at your fingertips all of the latest and most advanced financial models and methods, otherwise you will be toast. With his book, Dr. Javaheri has raised the entry level for authors in this field, providing the most sophisticated, modern tools and techniques you will need to stay ahead of the game."

—Paul Wilmott, founder, www.wilmott.com

"For an in-depth overview of stochastic volatility models, this book is a must-have for any quant, trader, academic, or student seriously interested in quantitative finance. Inside Volatility Arbitrage is loaded with useful, state-of-the-art information on stochastic volatility and calibration not found in any other book."

—Espen Gaarder Haug, options trader, JPMorgan

"To paraphrase Mark Twain, there are three kinds of risks: volatility, volatility of volatility, and the standard error of volatility of volatility. This comprehensive volume applies these fundamental concepts in providing an inside peek into the fascinating world of volatility trading and other sophisticated strategies. As such, this book will appeal to anyone whose lives are touched by uncertainty in the financial markets."

—Peter Carr, PhD, head of Quantitative Financial Research, Bloomberg LP Director of the Masters in Math Finance program, NYU

"Understanding the volatility smile requires finding the appropriate model for stock evolution, fitting its parameters to observed option prices, and examining the consistency between implied evolution and true evolution. Alireza Javaheri's book tackles all of these issues, with an especially comprehensive treatment of parameter estimation."

—Emanuel Derman, author of My Life as a Quant

Todays traders want to know when volatility is a sign that the sky is falling (and they should stay out of the market), and when it is a sign of a possible trading opportunity. Inside Volatility Arbitragecan help them do this. 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 used to trade the markets more profitably. Filled with in-depth insight and expert advice, Inside Volatility Arbitragewill help traders discover when "skewness" may present valuable trading opportunities as well as why it can be so profitable.

ALIREZA JAVAHERI, PhD, CFA, is an adjunct researcher in the Finance and Economics Department of Ecole des Mines de Paris. He has worked in the financial industry for many years with companies such as Citigroup, Lehman Brothers, and Goldman Sachs. He has written numerous articles in various financial journals.

Illustrations.

Acknowledgments.

Introduction.

Summary.

Contributions and Further Research.

Data and Programs.

Chapter 1: The Volatility Problem.

Introduction.

The Stock Market.

The Stock Price Process.

Historic Volatility.

The Derivatives Market.

The Black-Scholes Approach.

The Cox-Ross-Rubinstein Approach.

Jump Diffusion and Level-Dependent Volatility.

Jump Diffusion.

Level-Dependent Volatility.

Local Volatility.

The Dupire Approach.

The Derman-Kani Approach.

Stability Issues.

Calibration Frequency.

Stochastic Volatility.

Stochastic Volatility Processes.

GARCH and Diffusion Limits.

The Pricing PDE Under Stochastic Volatility.

The Market Price of Volatility Risk.

The Two-Factor PDE.

The Generalized Fourier Transform.

The Transform Technique.

Special Cases.

The Mixing Solution.

The Romano-Touzi Approach.

A One-Factor Monte Carlo Technique.

The Long-Term Asymptotic Case.

The Deterministic Case.

The Stochastic Case.

A Series Expansion on Volatility-of-Volatility.

Pure-Jump Models.

Variance Gamma.

Variance Gamma with Stochastic Arrival.

Variance Gamma with Gamma Arrival Rate.

Chapter 2: The Inference Problem.

Introduction.

Using Option Prices.

Direction Set (Powell) Method.

Numeric Tests.

The Distribution of the Errors.

Using Stock Prices.

The Likelihood Function.

Filtering.

The Simple and Extended Kalman Filters.

The Unscented Kalman Filter.

Kushner’s Nonlinear Filter.

Parameter Learning.

Parameter Estimation via MLE.

Diagnostics.

Particle Filtering.

Comparing Heston with Other Models.

The Performance of the Inference Tools.

The Bayesian Approach.

Using the Characteristic Function.

Introducing Jumps.

Pure Jump Models.

Recapitulation.

Model Identification.

Convergence Issues and Solutions.

Chapter 3: The Consistency Problem.

Introduction.

The Consistency Test.

The Setting.

The Cross-Sectional Results.

Robustness Issues for the Cross-Sectional Method.

Time-Series Results.

Financial Interpretation.

The Peso Theory.

Background.

Numeric Results.

Trading Strategies.

Skewness Trades.

Kurtosis Trades.

Directional Risks.

An Exact Replication.

The Mirror Trades.

An Example of the Skewness Trade.

Multiple Trades.

High Volatility-of-Volatility and High Correlation.

Non-Gaussian Case.

VGSA.

AWord of Caution.

Foreign Exchange, Fixed Income, and Other Markets.

Foreign Exchange.

Fixed Income.

References.

Index.