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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.

We propose a flexible yet tractable model of the term structure of interest rates (TSIR). Term structure models attempt to explain how interest rates depend on their maturities at a given point in time, characterizing the rela- tionship between short-term and long-term rates. Our model can reproduce and fit a variety of TSIR shapes by capturing cyclical fluctuations of interest rates, different monetary policy reactions as witnessed pre- and post-crisis as well as the effect of the business cycle or exogenous shocks. Our modelling approach also provides a characterization of long-term fluctuations in the mean level of interest rates unveiling the effects of monetary policy in- terventions in interest rates. Furthermore, using daily US data, we compare the empirical ability of our model to both fit and forecast the TSIR under different economic scenarios. We show that our model improves pricing and risk management by fitting and predicting interest rates more accurately and precisely than do existing TSIR models.