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We compute an analytical expression for the moment generating function of the joint random vector consisting of a spot price and its discretely monitored average for a large class of square-root price dynamics. This result, combined with the Fourier transform pricing method proposed by Carr and Madan [Carr, P., Madan D., 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4), Summer, 61-73] allows us to derive a closed-form formula for the fair value of discretely monitored Asian-style options. Our analysis encompasses the case of commodity price dynamics displaying mean reversion and jointly fitting a quoted futures curve and the seasonal structure of spot price volatility. Four tests are conducted to assess the relative performance of the pricing procedure stemming from our formulae. Empirical results based on natural gas data from NYMEX and corn data from CBOT show a remarkable improvement over the main alternative techniques developed for pricing Asian-style options within the market standard framework of geometric Brownian motion.

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We propose a constructive definition of electricity forward price curve with crosssectional timescales featuring hourly frequency on. The curve is jointly consistent with both risk-neutral market information represented by baseload and peakload futures quotes, and historical market information, as mirrored by periodical patterns exhibited by the time series of day-ahead prices. From a methodological standpoint, we combine nonparametric filtering with monotone convex interpolation such that the resulting forward curve is pathwise smooth and monotonic, cross-sectionally stable, and time local. From an empirical standpoint, we exhibit these features in the context of EPEX Spot and EEX Derivative markets. We perform a backtesting analysis to assess the relative quality of our forward curve estimate compared to the benchmark market model of Benth et al. (2007). 1

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