Hedging with Commodity Futures

Table of Contents

1 Introduction

2 Hedging Strategies

2.1 Risk Measures

2.1.1 Standard Deviation and Its Variance

2.1.2 VaR and CVaR

2.2 Optimization of Hedging Objective Functions

2.2.1 Minimum Variance Hedge

2.2.2 Minimum (C)VaR Hedge

3 Modeling Conditional Return Distribution

3.1 Relationship between Futures and Spot Prices

3.2 GARCH Models

3.2.1 GARCH (1,1)

3.2.2 Elliptical Distribution

3.2.3 Multivariate GARCH

3.3 Regime Switching Models

3.3.1 Markov Chains

3.3.2 Mixture of Distributions

3.3.3 MRS-Model

3.3.4 MRS-GARCH Model

4 Implementation

4.1 Description of the Data and Their Properties

4.1.1 Testing for Normality

4.1.2 Testing for ARCH Effects

4.1.3 Testing for Stationarity

4.1.4 Testing for Cointegration

4.2 Parameter Estimation

4.3 Estimation Results

4.4 Hedge Ratios

4.5 Hedging Effectiveness of the Hedging Strategy

5 Conclusion and Future Outlook

Research Objectives and Key Topics

This thesis aims to estimate Minimum Variance Hedge Ratios (MVHR) and Min-(C)VaR hedge ratios using diverse econometric models and to conduct a comparative analysis of their empirical performance in a portfolio setting.

• Comparison of various econometric hedging models (GARCH, MRS, OLS).
• Application of risk measures including Variance, VaR, and CVaR.
• Evaluation of hedging effectiveness using empirical crude oil data.
• Implementation of dynamic hedging strategies versus static OLS benchmarks.
• Analysis of market regimes and their impact on hedge ratios.

Excerpt from the Book

Summary of Chapters

1 Introduction: Defines commodity futures, explains the need for hedging against price risk, and outlines the thesis structure and research motivation.

2 Hedging Strategies: Introduces risk measures like Variance, VaR, and CVaR and details the optimization of objective functions for hedging.

3 Modeling Conditional Return Distribution: Discusses the statistical modeling of return distributions, specifically using GARCH and Regime Switching (MRS) models.

4 Implementation: Describes the empirical dataset, performs diagnostic tests (normality, stationarity, cointegration), and presents the parameter estimation and hedging results.

5 Conclusion and Future Outlook: Summarizes the key empirical findings and provides suggestions for potential future research extensions.

Keywords

Hedging, Commodity Futures, GARCH Models, Markov Regime Switching, Value at Risk, Conditional Value at Risk, Minimum Variance Hedge, Cointegration, Volatility, Risk Management, Crude Oil, Econometrics, Portfolio Optimization, Hedge Ratio, Hedging Effectiveness.

Frequently Asked Questions

What is the primary objective of this thesis?

The thesis aims to estimate and compare the empirical performance of Minimum Variance and Min-(C)VaR hedge ratios using several econometric models.

Which financial instruments are analyzed?

The study specifically focuses on crude oil spot and futures prices.

What research methodology is applied?

The author employs various econometric frameworks, including GARCH extensions (BEKK, CCC) and Markov Regime Switching (MRS) models, alongside a grid search method for hedge ratio selection.

What are the central thematic fields covered?

The research covers risk measures, hedging strategies, conditional return distribution modeling, and the empirical evaluation of hedging effectiveness.

What does the main part of the work entail?

The main part involves modeling the return distributions, estimating model parameters using crude oil data, and assessing the performance of different hedge ratios in an out-of-sample framework.

Which keywords best characterize this research?

Key terms include Hedging, GARCH, Markov Regime Switching, VaR, CVaR, Cointegration, and Volatility.

How is the path-dependency problem in MRS-GARCH models addressed?

The author discusses solving the path-dependency problem by employing a "recombining method" that collapses the conditional variances in each regime as suggested in the literature.

What did the empirical analysis regarding the static OLS model reveal?

The analysis showed that dynamic hedging models, while statistically sophisticated, did not significantly improve variance or VaR reduction compared to the static OLS model in the chosen dataset.

What is the significance of the HE/h* index mentioned?

This index accounts for both risk reduction and hedging costs, revealing that dynamic hedging strategies can be considerably more expensive than the simpler OLS approach.

Does the student's-t distribution improve model performance?

The study incorporates both normal and student's-t distribution assumptions for GARCH models to address potential tail risk, with BEKK-GARCH under the t-distribution performing above average.