Analysis of commodity prices with the particle filter

Aiube, Fernando Antônio Lucena; Baidya, Tara Keshar Nanda; Tito, Edison Americo Huarsaya

doi:10.1016/j.eneco.2006.06.006

Cited by 29 publications

(18 citation statements)

References 10 publications

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“…Empirical studies in these papers relate either to oil or to natural gas, where price spikes are not dominant. [17] uses a particle filter to estimate a two factor model with jumps and used the maximum likelihood method to obtain the model parameters.…”

Section: Introductionmentioning

confidence: 99%

Electricity futures price models: Calibration and forecasting

Islyaev

Date

2015

European Journal of Operational Research

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A new one factor model with a random volatility parameter is presented in this paper for pricing of electricity futures contracts. It is shown that the model is more tractable than multi-factor jump diffusion models and yields an approximate closed-form pricing formula for the electricity futures prices. On real market data, it is shown that the performance of the new model compares favorably with two existing models in the literature, viz. a two factor jump diffusion model and its jump free version, i.e., a two factor linear Gaussian model, in terms of ability to predict one day ahead futures prices. Further, a multi-stage procedure is suggested and implemented for calibration of the two factor jump diffusion model, which alleviates the difficulty in calibration due to a large number of parameters and pricing formulae which involve numerical evaluation of integrals. We demonstrate the utility of our new model, as well as the utility of the calibration procedure for the existing two factor jump diffusion model, by model calibration and price forecasting experiments on three different futures price data sets from Nord pool electricity data. For the jump diffusion model, we also investigate empirically whether it performs better in terms of futures price prediction than a corresponding, jump-free linear Gaussian model. Finally, we investigate whether an explicit calibration of jump risk premium in the jump diffusion model adds value to the quality of futures price prediction. Our experiments do not yield any evidence that modelling jumps leads to a better price prediction in electricity markets.

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Section: Introductionmentioning

confidence: 99%

Electricity futures price models: Calibration and forecasting

Islyaev

Date

2015

European Journal of Operational Research

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“…The model separates the spot price into two components-a short-term factor which captures any short-term deviations in prices as a result of short-term supply and demand fluctuations; and a long-term factor which represents the equilibrium price level and captures permanent changes in prices related to the cost of production. To name a few studies using the approach, Sørenson (2002) and Cartea and Williams (2008) Aiube, Baidya, and Tito (2008) extend the model by including a jump process in the short-term component.…”

Section: Short-/long-term Component Modelmentioning

confidence: 99%

Time‐varying market price of risk in the crude oil futures market

Bhar

Lee

2010

Journal of Futures Markets

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In this study, a three‐factor model of crude oil prices is estimated, which incorporates a time‐varying market price of risk. The model is able to accurately capture the term structure of futures prices with evidence suggesting that risk premiums in the crude oil market are time‐varying. Using the cross‐section of futures prices, we estimate a time‐series of the market price of risk in the crude oil market implied by the model. We find that the risk premiums in the crude oil market are driven by the same risk factors as equity and bond markets. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark 31:779–807, 2011

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“…Under this framework, we 3 compute closed-form expressions for the prices of futures contracts. 1 Energy markets present a perfect framework to analyse the suitability of models with a seasonal component as well as with long-term fluctuations in the mean reversion level. By nature, many sources of energy can be difficult to store or transport.…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 derives the posited model. Section 3 presents the empirical analysis, where subsections 3.3 and 3.4 present the in-sample and out-of-sample exercises, 1 We make no distinction between futures and forward agreements. 2 As described in the academic literature, most multi-factor models are hardly comparable to our model as they propose a stochastic convenience yield or a jump diffusion process.…”

Section: Introductionmentioning

confidence: 99%

“…The final regression, again subject to collinearity, achieves an explanatory power better than the regression on energy prices alone. 9 Finally, figure 6 presents a visual comparison of the results obtained using the energy market regression model (1) and the full regression model (5). Even though both models reproduce the evolution of long-term mean reversion prices quite well, it is clear that income and job market variables help to reduce the spikes present in the energy spot market, providing a much smoother and accurate representation of the long-term mean reversion process.…”

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Long-term swings and seasonality in energy markets

Moreno

Novales

Platania

2019

European Journal of Operational Research

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This paper introduces a two-factor continuous-time model for commodity pricing under the assumption that prices revert to a stochastic mean level, which shows smooth, periodic fluctuations over long periods of time. We represent the mean reversion price by a Fourier series with a stochastic component. We also consider a seasonal component in the price level, an essential characteristic of many commodity prices, which we represent again by a Fourier series. We obtain analytical pricing expressions for futures contracts. Using futures price data on Natural Gas, we provide evidence on the presence of long-term fluctuations and show how to estimate the long-term component simultaneously with a seasonal component using the Kalman filter. We analyse the in-sample and out-of-sample empirical performance of our pricing model with and without a seasonal component and compare it with the Schwartz and Smith (2000) model. Our findings show the in-sample and out-of-sample superiority of our model with seasonal fluctuations, thereby providing a simple and powerful tool for portfolio management, risk management, and derivative pricing. AbstractThis paper introduces a two-factor continuous-time model for commodity pricing under the assumption that prices revert to a stochastic mean level, which shows smooth, periodic fluctuations over long periods of time. We represent the mean reversion price by a Fourier series with a stochastic component. We also consider a seasonal component in the price level, an essential characteristic of many commodity prices, which we represent again by a Fourier series. We obtain analytical pricing expressions for futures contracts. Using futures price data on Natural Gas, we provide evidence on the presence of long-term fluctuations and show how to estimate the long-term component simultaneously with a seasonal component using the Kalman filter. We analyse the in-sample and out-of-sample empirical performance of our pricing model with and without a seasonal component and compare it with the Schwartz and Smith (2000) model. Our findings show the in-sample and out-of-sample superiority of our model with seasonal fluctuations, thereby providing a simple and powerful tool for portfolio management, risk management, and derivative pricing.

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Analysis of commodity prices with the particle filter

Cited by 29 publications

References 10 publications

Electricity futures price models: Calibration and forecasting

Electricity futures price models: Calibration and forecasting

Time‐varying market price of risk in the crude oil futures market

Long-term swings and seasonality in energy markets

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