THEMATIC PROGRAMS

November 21, 2014

April 9-10, 2010 Industrial-Academic Forum on Commodities, energy markets, and emissions trading

Talk Titles and Abstracts

René Aid (EDF, Université de Paris 9 Dauphine)
A structural risk-neutral model for electricity prices

The objective of this paper is to present a model for electricity spot prices and the corresponding forward contracts, which relies on the underlying market of fuels, thus avoiding the electricity non-storability restriction. The structural aspect of our model comes from the fact that the electricity spot prices depend on the dynamics of the electricity demand at the maturity T, and on the random available capacity of each production means. Our model explains, in a stylized fact, how the prices of different
fuels together with the demand combine to produce electricity prices. This modeling methodology allows one to transfer to electricity prices the risk-neutral probabilities of the market of fuels and under the hypothesis of independence between demand and outages on one hand, and prices of fuels on the other hand, it provides a regression-type relation between electricity forward prices and forward prices of fuels. Moreover, the model produces, by nature, the well-known peaks observed on electricity market data.

In our model, spikes occur when the producer has to switch from one technology to the lowest cost available one. Numerical tests performed on a very crude approximation of the French electricity market using only two fuels (gas and oil) provide an illustration of the potential interest of this model. This is a joint work with Luciano Campi, Adrien Nguyen Huu and Nizar Touzi.

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Alvaro Cartea (Universidad Carlos III & Madrid)
Mean reversion, measure changes and stochastic risk premia in commodity markets

The stylised facts of the behaviour of spot prices of commodities have been extensively studied. The main two features are: the presence of a seasonal trend; and that deviations from this trend, for instance jumps, tend to mean revert in the short-term. But what are the stylised facts under the risk-neutral measure? In this paper we set out to answer this question. We analyse how risk averse investors adjust the statistical measure of price dynamics when pricing risky securities written on commodities.

Spot (or day-ahead) price dynamics are much easier to model than dynamics under the risk-neutral measure because the former are observed whereas the latter can only be inferred from the price dynamics of instruments written on the spot commodity; for instance forward contracts. We model the market price of risk so that market participants bearing spot commodity risk are compensated for: jump arrival risk; jump size risk; and speed of mean reversion risk of both diffusion and/or jumps. Our approach can also be viewed as a special case of stochastic discount factors that not only affect the mean of the process but also its variance via the persistence of shocks to the economy.

We consider three models: the Schwartz (1997) pure diffusion model, the short- and long-term two-factor model of Schwartz and Smith (2000) and a three-factor arithmetic model that includes positive and negative jumps in the prices of commodities. We show that when spot dynamics exhibit mean reversion to a seasonal trend market participants are averse to deviations from this seasonal trend. Consequently, when pricing under the risk-adjusted measure agents will: over-state the time it takes to return to the seasonal trend; alter the mean of the process; and change the intensity of the jumps and their average size.

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Michael Coulon (Princeton University)
The Electricity Bid Stack: Linking the dynamics of fuel, power and carbon prices

Evidence from the PJM and New England electricity markets illustrates the benefit of using observed bid data to better understand the strong relationships between fundamental supply and demand factors and power prices. Exploiting the high correlation between movements of bids and fuel prices, we propose a parametric form for the bid stack function in order to construct a fundamental model for spot power prices. This approach allows for the investigation of possible merit order changes and fuel switching, which are considered key factors impacting prices of carbon emissions allowances. We therefore adapt the model to construct an equilibrium carbon price model, which can begin to capture the important but complicated dependence structure between CO2, electricity and other energy prices.

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Alex Eydeland (Morgan Stanley)
Commodity Modeling: View from the trenches

In this presentation we will present various issues and challenges facing commodity quants and suggest a number of modeling methodologies designed to address these issues. We will also give a brief introduction of standard commodity structures as well as new products and recent developments in commodity markets.

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Gilles Edouard Espinosa (Ecole Polytechnique)
A model of emissions and the price of carbon (joint with R. Carmona and N. Touzi)

Since the Kyoto Protocol, the carbon tax has aroused such a large interest from economists, financial analysts as well as mathematicians because its modelling is not classical. In this work, we propose a model consisting of n producers that have the ability to reduce their carbon emissions in return for a certain cost. We assume that they can also trade on the certificates market. Our aim is to determine the price of the carbon certificates, which will lead us to a forward-backward SDE with some irregularity. Using a method of approximation, we are able to show the existence and uniqueness of a solution. As expected, we find that with the introduction of such a tax, the emissions decrease.

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Max Fehr (London School of Economics)
Option Pricing in the European Unions Emission Trading Scheme

We propose a model for risk neutral futures price dynamics in the European Unions Emissions Trading Scheme (EU ETS). Historical price dynamics suggests that both allowance prices for different compliance periods and CER prices for different compliance periods are significantly related. To obtain a realistic price dynamics we take into account the specific details of the EU ETS compliance regulations, such as banking and the link to the Clean Development Mechanism (CDM), and exploit arbitrage relationships between futures on EU allowances and Certified Emission Reductions.

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Helyette Geman (Birbeck and ESCP Europ)
Inventory, Commodity Forward Curve and Spot price Volatility: The case of Crude Oil and Natural Gas

The role of inventory in explaining the shape of the forward curve and spot price volatility in commodity markets is central in the theory of storage developed by Kaldor (1939) and Working. Fama and French (1987) revisit the relationship between inventory and spot price volatility in the case of metals and use as a proxy for inventory the adjusted spread of the forward curve. The goal of our talk is threefold: i) review some interesting features of energy commodity forward curves in the recent past; ii)validate in the case of oil and natural gas the use of the slope of the forward curve as a proxy for inventory (the slope being defined in a way that filters out seasonality for natural gas); iii)) analyze directly for these two major commodities the relationship between inventory and price volatility. In agreement with the theory of storage, we find that a) the negative correlation between price volatility and inventory is globally significant for crude oil; b) this negative correlation prevails only during those periods of scarcity when the inventory is below the historical average and increases importantly during winter periods for natural gas. Our results are illustrated by the analysis of a 15 year-database of US oil and natural gas prices and inventories

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Georg Gruell (Duisburg-Essen)
Pricing CO2 permits using approximation approaches

Equilibrium models have been widely used in literature with the aim of showing theoretical properties of emission trading systems. First, a new equilibrium model is derived. Second, it is shown that the theoretical permit price is related to changes in the expectation of how long regulated companies will need to exhaust the remaining permits. Third, by application to real data we demonstrate that emission trading systems are inherently prone to jumps.

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Sebastian Jaimungal (University of Toronto)
A New Approach to Commodity Market Models

Market models and so-called string models for commodities have been widely used in industry. These approaches exactly match the current forward price term structure and traditionally model forward prices as multivariate GBMs. Here, I introduce a new approach where I model the discrete forward cost-of-carry directly rather than forward prices themselves. Through a sequence of measure changes, I demonstrate how to calibrate calendar spread options, options on forwards and forward prices all at once. Furthermore, I explain how unspanned stochastic volatility and jumps can be easily added into the modeling framework.

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Walid Mnif (University of Western Ontario)
Pricing and Hedging Strategies for Contingent Claims in an Incomplete Hybrid Emissions Market

We propose a stochastic approach for trading and pricing emission permits under an incomplete hybrid system in which credits are partially fungible from one period to another. Our approach is based on the filtering theory proposed by Follmer and Schweizer (1991). Under our framework exotic options can easily be priced with the use of straightforward derivatives pricing algorithms such as Monte Carlo simulation.

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Ehud Ronn (Morgan Stanley & Co.)
The Valuation and Information Content of Options on Crude-Oil Futures Contracts

Using market prices for crude-oil futures options and the prices of their underlying futures contracts, we estimate the volatility skew in two ways. As a benchmark for our theoretical model, on each date we first estimate a cross-sectional polynomial structure for each maturity to demonstrate the strength and weaknesses of a purely-mechanical model. We then apply to the empirical data a Merton-style jump-diffusion model, with a rich structure of cross-sectional constraints on the parameters. Both models are tested with respect to their mark-to-market accuracy over time, as well as their efficacy in hedging intertemporal option price changes. The postulated Merton-style model is shown to yield useful parameters from which market prices can be computed, option prices can be marked-to-market and (imperfectly) hedged, as well as an informationally-rich structure covering the time period of the turbulent past six months.

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Marliese Uhrig-Homburg (Universität Karlsruhe)
Understanding the Price Dynamics of Emission Permits: A Model for Multiple Trading Periods

Emission Trading Systems, like the EU Emission Trading System (EU ETS), are currently established in many different countries all over the world. Those are characterized by different regulatory rules which have shown to be appropriate in the recent past. The regulatory framework clearly impacts the characteristics of the spot price dynamics of such emission permits, a dependency not yet fully understood. In fact, there exists no theoretical model accounting for the main stylized facts like the existence of multiple trading periods, the allowance of banking, and the later delivery of lacking certificates, although insights into this subject are worthy for risk management, derivative pricing, and energy-related investment decisions. Therefore, we develop a dynamic stochastic equilibrium model for multiple trading periods, which makes it possible to account for those features. We present a solution for the equilibrium spot price and analyze the spot price dynamics and volatilities as well as sensitivities towards market design parameters. Moreover, we can show that the spot price can be subdivided into different ratios, each one resulting from one trading period of a particular setting.

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