Long-term swings and seasonality in energy markets

This paper introduces a two-factor continuous-time model for commodity pricing under the assump- tion 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 si- multaneously 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

Estimating and pricing commodity futures with time‐delay stochastic processes

Producción CientíficaIn commodity futures pricing models, the commodity present price is gener-ally considered to reflect all information in the markets and past information isnot regarded important. However, there is some empirical evidence that showsthat this fact is unrealistic. In this paper, we consider some stochastic mod-els with delay for pricing commodity futures. The functions of the commodityprice stochastic process under the risk-neutral measure are necessary for pricingderivatives. However, the observations in the market have risk. Then, we use atechnique that allows us to estimate the functions of the risk-neutral commodityspot price stochastic process, directly from futures prices traded in the market,and show how to price the commodity futures. Finally, we make an empiricalapplication of this methodology with gold futures traded in the COMEX. Fur-thermore, we make clear the supremacy of the delay models in pricing goldfutures.Agencia Estatal de Investigación,(Grant/Award Number:PID2020-113554GB-I00/AEI/10.13039/501100011033)unta de Castilla y León and European FEDER (Funds,Grant/Award Number: VA193P20

Valoración de Contratos de futuros sobre energía eléctrica en el polo español del mercado ibérico de energía

El precio de la energía eléctrica, debido a sus características especiales, presenta un comportamiento extremadamente volátil, por tanto, su riesgo debe ser gestionado y mitigado por los participantes del mercado. Sobre este trasfondo, en este trabajo presentamos dos modelos para la valoración y predicción de los precios de los contratos de futuros y obtenemos una expresión cerrada para su valoración. En ambos modelos suponemos que el precio de este futuro depende del precio spot de la electricidad, cuya dinámica viene dada, en el primer caso, por un proceso geométrico, y en el segundo sigue un proceso con reversión a la media que recoge la posible estacionalidad a lo largo del año (a través de una serie de Fourier). Analizamos el comportamiento de los modelos con y sin estacionalidad, comparando los precios estimados con los observados en el mercado a plazo MEFF Power para el periodo 2015-2019. De este estudio, se desprende que considerar reversión a la media y estacionalidad en los modelos de valoración de futuros ofrece precios más próximos a los observados, tanto en el periodo de estimación como de predicción considerados. Por tanto, creemos que la expresión obtenida en este trabajo para la valoración de los futuros sobre la electricidad en el Mercado Ibérico Español, teniendo en cuenta la reversión a la media y estacionalidad, supone una contribución interesante para los gestores que tratan de manejar el riesgo en todos los segmentos de la industria de electricidad.The electricity price, due to its special characteristics, has an extremely volatile behaviour. Therefore, its risk must be managed and mitigated by market participants. Against the current backdrop, in this paper, we show two pricing models for the valuation and prediction of electricity futures contracts, for that we obtain a closed-form expression. In both models, the future price is assumed to depend on the electricity spot price, which follows a geometric Brownian Motion process and one of them, also follow a mean reversion process, which collects the possible seasonality throughout the year, by introducing a Fourier series. The behavior of both models, with and without seasonality, were analyzed by comparing the prices obtained with those traded from 2015 to 2019 in the MEFF Power. The present study suggests that considering mean reversion and the seasonality as a component in pricing models offers prices closer to those traded in both periods considered - estimation and forecasting period. Therefore, we believe that the closed-form expression obtained in this paper for the valuation of electricity futures traded at Spanish Iberian Market, represents an interesting contribution for managers when managing risk in all segments of the electricity industry.Departamento de Economía AplicadaMáster en Análisis Económico y Finanza