Spot Price Dynamics Research Articles

A Partially Linear Approach to Modelling the Dynamics of Spot and Futures Prices

In this paper we consider the dynamics of spot and futures prices in the presence of arbitrage. We propose a partially linear error correction model where the adjustment coefficient is allowed to depend non-linearly on the lagged price difference. We estimate our model using data on the DAX index and the DAX futures contract. We find that the adjustment is indeed nonlinear. The linear alternative is rejected. The speed of price adjustment is increasing almost monotonically with the magnitude of the price difference.

Integrating Multiple Commodities in a Model of Stochastic Price Dynamics

In this paper we develop a multi-factor model for the joint dynamics of related commodity spot prices in continuous time. We contribute to the existing literature by simultaneously considering various commodity markets in a single, consistent model. In an application we show the economic significance of our approach. We assume that the spot price processes can be characterized by the weighted sum of latent factors. Employing an essentially-affine model structure allows for rich dependencies among the latent factors and thus, the commodity prices. The co-integrated behavior between the different spot price dynamics is explicitly taken into account. Within this framework we derive closed-form solutions of futures prices. The Kalman Filter methodology is applied to estimate the model for crude oil, heating oil and gasoline futures contracts traded on the NYMEX. Empirically, we are able to identify a common non-stationary equilibrium factor driving the long-term price behavior and stationary factors affecting all three markets in a common way. Additionally, we identify factors which only impact subsets of the commodities considered. To demonstrate the economic consequences of our integrated approach, we evaluate the investment into a refinery from a financial management perspective and compare the results with an approach neglecting the co-movement of prices. This negligence leads to radical changes in the project's assessment.

A Partially Linear Approach to Modelling the Dynamics of Spot and Futures Prices

This paper considers the dynamics of spot and futures prices in the presence of arbitrage. A partially linear error correction model is proposed where the adjustment coefficient is allowed to depend non-linearly on the lagged price difference. The model is estimated using data on the DAX index and the DAX futures contract. We find that the adjustment is indeed nonlinear. The linear alternative is rejected. The speed of price adjustment is increasing almost monotonically with the magnitude of the price difference.

Electricity spot price dynamics: Beyond financial models

We reveal properties of electricity spot prices that cannot be captured by the statistical models, commonly used to model financial asset prices, that are increasingly used to model electricity prices. Using more than eight years of half-hourly spot price data from the New Zealand Electricity Market, we find that the half-hourly trading periods fall naturally into five groups corresponding to the overnight off-peak, the morning peak, daytime off-peak, evening peak, and evening off-peak. The prices in different trading periods within each group are highly correlated with each other, yet the correlations between prices in different groups are lower. Models, adopted from the modeling of security prices, that are currently applied to electricity spot prices are incapable of capturing this behavior. We use a periodic autoregression to model prices instead, showing that shocks in the peak periods are larger and less persistent than those in off-peak periods, and that they often reappear in the following peak period. In contrast, shocks in the off-peak periods are smaller, more persistent, and die out (perhaps temporarily) during the peak periods. Current approaches to modeling spot prices cannot capture this behavior either.

Market price of risk implied by Asian-style electricity options and futures

In this paper we propose a jump-diffusion type model which recovers the main characteristics of electricity spot price dynamics in the Nordic market, including seasonality, mean-reversion and spiky behavior. We show how the calibration of the market price of risk to actively traded futures contracts allows for efficient valuation of Nord Pool's Asian-style options written on the spot electricity price. Furthermore, we study the evolution of the market price of risk (and the risk premium) over a three year time period and compare the obtained results with those reported in the literature.

A Non‐Gaussian Ornstein–Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing

A mean‐reverting model is proposed for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non‐Gaussian Ornstein–Uhlenbeck processes with jump processes giving the normal variations and spike behaviour of the prices. The amplitude and frequency of jumps may be seasonally dependent. The proposed dynamics ensures that spot prices are positive, and that the dynamics is simple enough to allow for analytical pricing of electricity forward and futures contracts. Electricity forward and futures contracts have the distinctive feature of delivery over a period rather than at a fixed point in time, which leads to quite complicated expressions when using the more traditional multiplicative models for spot price dynamics. In a simulation example it is demonstrated that the model seems to be sufficiently flexible to capture the observed dynamics of electricity spot prices. The pricing of European call and put options written on electricity forward contracts is also discussed.

Evaluating the Empirical Performance of Alternative Econometric Models for Oil Price Forecasting

The relevance of oil in the world economy explains why considerable effort has been devoted to the development of different types of econometric models for oil price forecasting. Several specifications have been proposed in the economic literature. Some are based on financial theory and concentrate on the relationship between spot and futures prices (financial models). Others assign a key role to variables explaining the characteristics of the physical oil market (structural models). The empirical literature is very far from any consensus about the appropriate model for oil price forecasting that should be implemented. Relative to the previous literature, this paper is novel in several respects. First of all, we test and systematically evaluate the ability of several alternative econometric specifications proposed in the literature to capture the dynamics of oil prices. Second, we analyse the effects of different data frequencies on the coefficient estimates and forecasts obtained using each selected econometric specification. Third, we compare different models at different data frequencies on a common sample and common data. Fourth, we evaluate the forecasting performance of each selected model using static and dynamic forecasts, as well as different measures of forecast errors. Finally, we propose a new class of models which combine the relevant aspects of the financial and structural specifications proposed in the literature (mixed models). Our empirical findings can be summarized as follows. Financial models in levels do not produce satisfactory forecasts for the WTI spot price. The financial error correction model yields accurate in-sample forecasts. Real and strategic variables alone are insufficient to capture the oil spot price dynamics in the forecasting sample. Our proposed mixed models are statistically adequate and exhibit accurate forecasts. Different data frequencies seem to affect the forecasting ability of the models under analysis.

The Nature of Power Spikes: A Regime-Switch Approach

textabstractDue to its non-storable nature, electricity is a commodity with probably the most volatile spot prices, exemplified by occasional spikes. Appropriate pricing, portfolio, and risk management models have to incorporate these characteristics, and the spikes in particular. We investigate the nature of power spikes in a number of different markets. We test what time-series model is best able to capture the dynamics of these disruptive spot prices. We use regime-switching models to infer whether the price spikes should be treated as abnormal and independent deviations from the ‘normal’ price dynamics or whether they form an integral part of the price process. We test the time-series models on day-ahead markets in Europe and the US. We find that regimeswitch models are better able to capture the market dynamics than a GARCH(1,1) or Poisson jump model. We also find clear differences between the markets and attribute part of the differences to the share of hydro-power in the total supply stack: hydro-power serves as an indirect means to store electricity, which has a dampening effect on spikes.

Valuation and Optimal Operation of Electric Power Plants in Competitive Markets

We present an algorithm for the valuation and optimal operation of hydroelectric and thermal power generators in deregulated electricity markets. Real options theory is used to derive nonlinear partial-integro-differential equations (PIDEs) for the valuation and optimal operating strategies of both types of facilities. The equations are designed to incorporate a wide class of spot price models that can exhibit the same time-dependent, mean-reverting dynamics and price spikes as those observed in most electricity markets. Particular attention is paid to the operational characteristics of real power generators. For thermal power plants, these characteristics include variable start-up times and costs, control response time lags, minimum generating levels, nonlinear output functions, and structural limitations on ramp rates. For hydroelectric units, head effects and environmental constraints are addressed. We illustrate the models with numerical examples of a pump storage facility and a thermal power plant. This PIDE framework can achieve high levels of computational speed and accuracy while incorporating a wide range of spot price dynamics and operational characteristics.

THE NORMAL INVERSE GAUSSIAN DISTRIBUTION AND SPOT PRICE MODELLING IN ENERGY MARKETS

We model spot prices in energy markets with exponential non-Gaussian Ornstein–Uhlenbeck processes. We generalize the classical geometric Brownian motion and Schwartz' mean-reversion model by introducing Lévy processes as the driving noise rather than Brownian motion. Instead of modelling the spot price dynamics as the solution of a stochastic differential equation with jumps, it is advantageous from a statistical point of view to model the price process directly. Imposing the normal inverse Gaussian distribution as the statistical model for the Lévy increments, we obtain a superior fit compared to the Gaussian model when applied to spot price data from the oil and gas markets. We also discuss the problem of pricing forwards and options and outline how to find the market price of risk in an incomplete market.

High Frequency Electricity Spot Price Dynamics: An Intra-Day Markets Approach

In this paper we develop a new approach to understanding the behavior of high frequency electricity spot prices. It treats electricity delivered at different times of the day as different commodities, while recognizing that these commodities may be traded on a small number of intra-day markets. We first present a detailed analysis of the high frequency dynamics of prices at a key New Zealand node. Our analysis, which includes the use of a periodic autoregression model, supports the treating of electricity as multiple commodities and also reveals intrinsic correlation properties that indicate the existence of distinct intra-day markets. Conventional models cannot adequately capture properties that have important implications for derivative pricing and real options analysis. We therefore extend the literature by introducing a state space model of high frequency spot prices that preserves this intra-day market structure.

Pricing and Hedging Spread Options

We survey theoretical and computational problems associated with the pricing and hedging of spread options. These options are ubiquitous in the financial markets, whether they be equity, fixed income, foreign exchange, commodities, or energy markets. As a matter of introduction, we present a general overview of the common features of all spread options by discussing in detail their roles as speculation devices and risk management tools. We describe the mathematical framework used to model them, and we review the numerical algorithms actually used to price and hedge them. There is already extensive literature on the pricing of spread options in the equity and fixed income markets, and our contribution is mostly to put together material scattered across a wide spectrum of recent textbooks and journal articles. On the other hand, information about the various numerical procedures that can be used to price and hedge spread options on physical commodities is more difficult to find. For this reason, we make a systematic effort to choose examples from the energy markets in order to illustrate the numerical challenges associated with these instruments. This gives us a chance to discuss an interesting application of spread options to an asset valuation problem after it is recast in the framework of real options. This approach is currently the object of intense mathematical research. In this spirit, we review the two major avenues to modeling energy price dynamics. We explain how the pricing and hedging algorithms can be implemented in the framework of models for both the spot price dynamics and the forward curve dynamics.