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Description of Inside Volatility Arbitrage

Today's 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 Arbitrage" can 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 Arbitrage" will help traders discover when 'skewness' may present valuable trading opportunities as well as why it can be so profitable.

Title Information

ISBN:

9780471733874

Pages:

272 pages

Format:

Hardback

Product Code:

21188

Publisher:

John Wiley & Sons Inc

Published:

07/10/2005

Edition:

illustrated edition

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About

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.

Contents of Inside Volatility Arbitrage

Provisional contents:

Introduction
Summary
Contributions and Further Research
Data and Programs

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
- Link to Credit Spread
- Level Dependent Volatility
- The Constant Elasticity Variance Approach
- The Bensoussan Crouhy Galai Approach

Local Volatility
- The Dupire Approach
- The Breeden \& Litzenberger Identity
- The Dupire Identity
- Local Volatility vs Instantaneous Volatility
- 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
- Remark on the Gamma Distribution
- Stochastic Volatility vs Time-Changed processes
- Variance Gamma with Stochastic Arrival
- Option Pricing under VGSA
- The Characteristic Function
- Variance Gamma with Gamma Arrival Rate


The Inference Problem

Introduction

Using Option Prices
- Direction Set (Powell) Method
- Numeric Tests
- The Distribution of the Errors

Using Stock Prices
- The Likelihood Function
- The Justification for the MLE
- Likelihood Evaluation and Filtering
- Filtering
- Interpretation of the Kalman Gain
- The Simple and Extended Kalman Filters
- Another Interpretation of the Kalman Gain
- Residuals, MPE and RMSE
- The Unscented Kalman Filter
- Kushner's Non-Linear Filter
- Details of the Kushner algorithm
- Parameter Learning
- An Illustration
- Joint Filtering Examples
- Observability
- The One-Dimensional State within the Joint Filter
-- Joint Filters and Time Interval
- Parameter Estimation via MLE
- An Illustration
- Stochastic Volatility Examples
- Optimization-Constraints for the Square-Root Model
- An Alternative Implementation
- The One-Dimensional State
- Other stochastic volatility models
- Diagnostics
- Chi-Square Test
- Box-Ljung Test
- Test Results
- Variogram
- Particle Filtering
- Underlying Theory
- Resampling
- Implementation
- An Illustration
- Application to the Heston Model
- Test Results
- Error Size
- The MH Enhancement
- Comparing Heston with other Models
- The Models
- The Results
- Parameter Learning Revisited
- The Performance of the Inference Tools
- Sample Size
- Joint Estimation of the Parameters
- Error Size revisited
- High Frequency Data
- The Frequency of the Observations
- Sampling Distribution
- The Bayesian Approach
- The Gibbs Sampler
- A Simple Illustration
- The Metropolis-Hastings Algorithm
- Illustration
- A Few Distributions
- Regression Analysis
- Application to Gaussian SV Models (Heston)
- Using the Characteristic Function
- Introducing Jumps
- The Model
- The Generic Particle Filter
- Extended/ Unscented Particle Filters
- The Srivastava Approach
- Numeric results
- The Optimization Algorithm
- Pure-Jump Models
- VG
- VGSA
- The Filtering Algorithm
- Parameter Estimation
- A More Efficient Algorithm
- An Extended/ Unscented Particle Filter
- Numeric Results
- Diagnostics
- VGG
- A Bayesian Approach for VGSA

Recapitulation
- Model Identification
- Convergence Issues and Solutions


The Consistency Problem

Introduction

The Consistency Test
- The Setting
- The Cross-Sectional Results
- Robustness Issues for the Cross-Sectional Method
- Time-Series Results
- Robustness Issues for the Time-Series Method
- Financial Interpretation

The "Peso'' Theory

- Background
- Numeric Results

Trading Strategies
- Skewness Trades
- Kurtosis Trades
- Directional Risks
- Skewness vs Kurtosis
- An Exact Replication
- The Mirror Trades
- An Example of the Skewness Trade
- The Options Bid-Ask Spread
- Early Termination
- Implied Volatility Term-Structure
- Which Hedge-Ratio should we use?
- Multiple Trades
- High Volatility-of-Volatility and High Correlation

Non-Gaussian Case
- VGSA
- VGSA vs VG
- Cross-Sectional vs Time-Series VGSA

A Word of Caution

Foreign Exchange, Fixed Income and Other Markets
- Foreign Exchange
- Fixed Income
- The Time-Series
- The Cross-Section

Bibliography