Inside Volatility Arbitrage

The Secrets of Skewness

By: Alireza Javaheri

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Product code: 21188
ISBN: 0471733873
384 pages
Format: Hb
Published by: John Wiley & Sons, 2005

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Inside Volatility Arbitrage - front page cover image

Inside Volatility Arbitrage - Chapter headings

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