Commodity Derivatives Research Articles

Markov Models for Commodity Futures: Theory and Practice

This objective of this paper is to develop a generic, yet practical framework for construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by spikes in the spot process. In the first, largely theoretical, part of the paper we derive a series of useful results about low-dimensional Markov representation of the dynamics of an entire term structure of futures prices. Extending previous results in the literature, we cover jump-diffusive models with stochastic volatility as well as several classes of regime-switch models. To demonstrate the process of building models for a specific commodity market, the second part of the paper applies a selection of our theoretical results to the exercise of constructing and calibrating derivatives trading models for USD natural gas. Special attention is paid to the incorporation of empirical seasonality effects in futures prices, in implied volatilities and their smile, and in correlations between futures contracts of different maturities. European option pricing in our proposed gas model is closed-form and of the same complexity as the Black-Scholes formula.

Food commodity derivatives: a new cause of malnutrition?

Food commodity derivatives: a new cause of malnutrition?

A multi-factor jump-diffusion model for commodities†

In this paper we develop an arbitrage-free model for the pricing of commodity derivatives. The model generates futures (or forward) commodity prices consistent with any initial term structure. The model is consistent with mean reversion in commodity prices and also generates stochastic convenience yields. Our model is a multi-factor jump-diffusion model, one specification of which allows the prices of long-dated futures contracts to jump by smaller magnitudes than short-dated futures contracts, which, to our knowledge, is a feature that has not previously appeared in the literature, in spite of it being in line with stylised empirical observations (especially for energy-related commodities). Our model also allows for stochastic interest rates. The model produces semi-analytic solutions for standard European options, which enable option prices to be evaluated in typically about 1/50th of a second (depending upon parameter values and the required accuracy). This opens the possibility to calibrate the model parameters by deriving implied parameters from the market prices of options. We perform such a calibration on crude oil options and show that, allowing long-dated futures contracts to jump by smaller magnitudes than short-dated contracts, gives a greatly enhanced fit. †This is a condensed and enhanced version of a previous working paper (Crosby 2005) entitled “Commodities: a simple multi-factor jump-diffusion model”.

Commodity Derivative Market and its Impact on Spot Market

Nation wide trading in commodities futures in India was introduced for many agricultural commodities and later trading in futures was banned for few commodities due to pressure on spot prices of these commodities. The paper studies the impact of futures trading in three important commodities which were banned by the government from trading in futures and their impact on spot prices. The study uses simple linear regressions, correlations, Granger Causality tests to find the answer. The study also tries to find if the seasonal/cyclical fluctuations in these commodities prices have been affected by the introduction of futures in those commodities. Hodrick-Prescott filter is used to differentiate the general trend and seasonal/cyclical fluctuations in prices. The study finds that in India future trading in the selected commodities had apparently led to increase in prices of commodities like urad. It also increased the volatilities in the spot market.

Commodity Futures Markets in India: Riding the Growth Phase

Commodity derivatives play a pivotal role in the price risk management process especially in any agricultural surplus country. As unique hedging instruments derivatives such as forwards, futures, swaps, options and exotic derivative products are extensively used in the global market. However, Indian market is limited to commodity futures only. The present study is an investigation into the present status, growth constraints and developmental policy alternatives for commodity futures markets in India. The study has surveyed the various publicly available websites of recognized commodity exchanges and their organizational and the regulatory set up for futures trading. Also, as the factors that drive commodity prices are observed to be different from the factors that drive equity prices, commodities are perceived to be effective diversifying agents. This study explores the advantages of adding commodities to a portfolio of equities in Indian context based on empirical data and quantifies the diversification benefit and downside risk protection the commodities offer in portfolio context. The study concluded that the less-than-perfect or negative correlation of commodities with equities makes them an excellent candidate for diversification. This diversification benefit was demonstrated in two ways. First, it was observed that by adding commodity futures to a portfolio of equities enhance the risk-adjusted return of a portfolio. Second, it was observed that adding commodity futures to equity portfolios provides a significant downside protection and enhances skewness and kurtosis of the return distribution.

Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives

Commodity derivatives are becoming an increasingly important part of the global derivatives market. Here we develop a tractable stochastic volatility model for pricing commodity derivatives. The model features unspanned stochastic volatility, quasi-analytical prices of options on futures contracts, and dynamics of the futures curve in terms of a low-dimensional affine state vector. We estimate the model on NYMEX crude oil derivatives using an extensive panel data set of 45,517 futures prices and 233,104 option prices, spanning 4082 business days. We find strong evidence for two, predominantly unspanned, volatility factors.

The Need for Transparency in Commodity and Commodity Derivatives Markets

This paper argues that transparency-boosting measures specifically tailored to commodity and commodity derivatives markets are much needed. In particular, encouraging the creation of a clearing infrastructure for OTC commodity and commodity derivatives markets would be desirable. Moreover, EU regulators should consider setting up a new, more effective market abuse regime aimed at preventing manipulation in both the physical and financial commodities markets. Finally, in cooperation with the G20, EU authorities should consider the creation of an International Commodity Agency to increase transparency and restore confidence in international physical markets for commodities. The paper is structured as follows: Section 2 briefly discusses the fundamentals of commodity spot and futures markets. Section 3 presents both physical commodity markets and commodity derivative markets in their usual breakdown categories: agriculture, metals and energy. Section 4 discusses the regulations in the EU and the US concerning commodity derivatives. Section 5 advances certain policy proposals and the last section draws the conclusions.

Unspanned Stochastic Volatility and the Pricing of Commodity Derivatives

We conduct a comprehensive analysis of unspanned stochastic volatility in commodity markets in general and the crude-oil market in particular. We present model-free results that strongly suggest the presence of unspanned stochastic volatility in the crude-oil market. We then develop a tractable model for pricing commodity derivatives in the presence of unspanned stochastic volatility. The model features correlations between innovations to futures prices and volatility, quasi-analytical prices of options on futures and futures curve dynamics in terms of a low-dimensional affine state vector. The model performs well when estimated on an extensive panel data set of crude-oil futures and options.

Institutional Investors in Indian Commodity Derivative Markets - Prospects for the Future

The Government of India is contemplating allowing the Institutional investors like Foreign Institutional Investors, Mutual funds and Banks to trade in a few selected products of commodity derivatives markets in India. This paper argues that if the institutional investors are allowed to operate in all the products of the commodity derivative markets, it has implications for both the liquidity and broad basing of commodity derivatives markets given the assets under management of these investors. Their entry into commodity derivatives markets is also expected to benefit them given the portfolio diversification opportunities. This paper discusses the implications of the grant of permission to these institutional investors to operate in commodity derivative markets.

PRICING FLOW COMMODITY DERIVATIVES USING FIXED INCOME MARKET TECHNIQUES

In this work, the valuation of energy-related financial contracts written on prices of flow commodities (such as natural gas, oil and electrical power) will be elaborated. Due to restrictions on storability of the underlying, the pricing of flow commodity derivatives is not trivial and thus correct valuation is still under discussion. In this paper, an axiomatic setting is followed, which provides a connection to interest rate theory, whose toolkit we utilize to consistently price frequently quoted flow commodity options such as caps, floors, collars and cross commodity spreads.

Héylette Geman: Commodities and Commodity Derivatives - Modeling and Pricing for Agriculturals, Metals and Energy

Héylette Geman: Commodities and Commodity Derivatives - Modeling and Pricing for Agriculturals, Metals and Energy

Option value of electricity demand response

As electricity markets deregulate and energy tariffs increasingly expose customers to commodity price volatility, it is difficult for energy consumers to assess the economic value of investments in technologies that manage electricity demand in response to changing energy prices. The key uncertainties in evaluating the economics of demand–response technologies are the level and volatility of future wholesale energy prices. In this paper, we demonstrate that financial engineering methodologies originally developed for pricing equity and commodity derivatives (e.g., futures, swaps, options) can be used to estimate the value of demand-response technologies. We adapt models used to value energy options and assets to value three common demand–response strategies: load curtailment, load shifting or displacement, and short-term fuel substitution—specifically, distributed generation. These option models represent an improvement to traditional discounted cash flow methods for assessing the relative merits of demand-side technology investments in restructured electricity markets.

Investigating the Determinants of the Decision to Engage In a Corporate Hedging Strategy

This paper investigates the decision to engage in a comprehensive corporate hedging strategy for Australian listed companies. Specifically the pursuit of a comprehensive hedging strategy is gauged by jointly investigating the corporate use of foreign currency derivatives; interest rate derivatives; commodity derivatives and foreign debt. The results show that firm size, leverage, dividend yield and block holdings are incentive factors to the comprehensive hedging decision, while executive shares is a disincentive factor. Consistent with hedging theory, the significance of the leverage variables supports the financial distress cost hypothesis. Support is also found for the dividend decision is a substitute for corporate hedging.

The use of multiple risk management strategies: evidence from the natural gas industry

Starting in 1978 and continuing throughout the 1980s, natural gas pipelines faced a series of regulatory changes, including price deregulation, which changed their exposures to price and quantity risk. We exploit this unique environment and examine cross-sectional and time-series patterns in the use of multiple risk management strategies by pipeline companies. Natural gas pipelines use a combination of such strategies, including gas storage, cash holdings, line-of-business and geographic diversification, and commodity derivatives to hedge their increasing risks. Gas storage shows a complementary relation to holding cash and using derivatives to mitigate these risks. However, differences in the financial characteristics of derivatives hedgers and storage hedgers suggest that firms use derivatives to manage price risk and store gas to manage volume risk. Derivatives hedgers are similar to firms that diversify. In addition, firms that engage in hedging activities have smaller and less variable sensitivities to price changes than firms that do not, especially post-deregulation.

Migration of price discovery in semiregulated derivatives markets

AbstractThis study investigates the information content of futures option prices when the underlying futures price is regulated and the futures option price is not. The New York Board of Trade (NYBOT) provides the empirical setting for this regulatory mismatch. Many commodity derivatives markets regulate the prices of all derivatives on a single underlying commodity simultaneously. Some exchanges, including the NYBOT, regulate only their futures contracts, leaving the options on these futures contracts unregulated. This study takes a particular interest in the option‐implied futures price when the observed futures price is locked limit. © 2006 Wiley Periodicals, Inc. Jrl Fut Mark 26:209–241, 2006

Drift matters: An analysis of commodity derivatives

This article presents a reduced-form, two-factor model to price commodity derivatives, which generalizes the model by Schwartz and Smith (2000). The model allows for two mean-reverting stochastic factors and therefore implies that spot and futures prices can be stationary. An empirical study for the crude oil market tests the new model. Out-of-sample pricing and hedging results for futures and forwards show that the new model dominates the nonstationary model by Schwartz and Smith in the following sense: It works equally well for short-term contracts but leads to major improvements for long-term contracts. This finding is particularly relevant for typical applications like the valuation of commodity-linked real assets with long maturities. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:211–241, 2005

Valuation of Commodity Derivatives with an Unobservable Convenience Yield

This paper extends, by developing a three-factor model, the existing literature on commodity derivatives to account for an unobservable stochastic convenience yield. The latter is not observable, but investors can draw inferences about it by observing the spot commodity price and the instantaneous interest rate. Investors operate in an economy with incomplete information. Quasi-analytical formulas for forward and futures prices, and closed-form solutions for options on forward and futures contracts are obtained. Numerical illustration allows comparing the model of this paper (incomplete information) to that of Schwartz's (1997). The two models provide similar futures prices for short maturities, but the Schwartz model prices may be higher than those of the incomplete information model for longer maturities. The incomplete information model, relative to the Schwartz model, has the tendency to overprice options for low volatilities of the three variables and to under price options for high volatilities. Moreover, for out of the money options, values between the two models diverge substantially.

Drift Matters: An Analysis of Commodity Derivatives

This paper presents a reduced form affine two-factor model to price commodity derivatives, which generalizes the model by Schwartz & Smith (2000). The model allows for two mean-reverting stochastic factors, and therefore implies that spot and futures prices can be stationary. An empirical study for the crude oil market tests the new model. Out-of sample pricing and hedging results for futures and forwards show that the new model dominates the nonstationary model by Schwartz & Smith in the following sense: It works equally well for short-term contracts, but leads to major improvements for long-term contracts. This finding is particularly relevant for typical applications like the valuation of commodity-linked real assets with long maturities.

Valuation of commodity derivatives in a new multi-factor model

This paper extends existing commodity valuation models to allow for stochastic volatility and simultaneous jumps in the spot price and spot volatility. Closed-form valuation formulas for forwards, futures, futures options, geometric Asian options and commodity-linked bonds are obtained using the Heston (1993) and Bakshi and Madan (2000) methodology. Stochastic volatility and jumps do not affect the futures price at a given point in time. However, numerical examples indicate that they play important roles in pricing options on futures.

Exotic electricity options and the valuation of electricity generation and transmission assets

We present and apply a methodology for valuing electricity derivatives by constructing replicating portfolios from electricity futures and the risk-free asset. Futures-based replication is made necessary by the non-storable nature of electricity, which rules out the traditional spot market, storage-based method of valuing commodity derivatives. Using the futures-based approach, valuation formulae are derived for both spark and locational spread options for both geometric Brownian motion and mean reverting price processes. These valuation results are in turn used to construct real options-based valuation formulae for generation and transmission assets. Finally, the valuation formula derived for generation assets is used to value a sample of assets that have been recently sold, and the theoretical values calculated are compared to the observed sales prices of the assets.