Gas Fire Power Plant Management Through Numerical Approximation of Spark Spread Options
Babacar Seck, Anas Abdullah
TL;DR
This work addresses the problem of valuing gas-fired power plants through spark spread options when electricity and gas prices follow jump-diffusion dynamics. It develops a two-factor mean-reverting framework with jumps for spot prices and presents multiple pricing approaches, ranging from double-integral and Kirk-based approximations to closed-form solutions under correlation-assessing simplifications and linear dependencies between forwards. Key contributions include a Carmona-Durrleman-style jump approximation for daily spark spreads, a practical double-integral algorithm with convergence properties, and tractable closed-form formulas for both no-jump and jump scenarios within a linear forward-dependency setting. The results offer implementable, cross-commodity valuation tools suitable for incomplete energy markets and have potential applicability to forward curves, emissions costs, and plant-management decisions in real-world energy pools such as the Alberta market.
Abstract
Cross-commodity valuation approaches to value gas fire power plants are well studied in the literature. Hence, the value of the gas fire power plant is identical to the value of a spark spread option wherein the underlying are electricity and gas with a strike price assimilated to operating and maintenance costs. Power and fuels spot prices account for uncertain futures cash-flows for power-plant generator owners. For instance, for gas-fired turbine plant, spot prices of electricity and gas determine the random cash-flows of the power-plant. Other than the spot prices, the valuation of such plant involves among other deterministic cost the plant heat rate and operating costs. Recently, the cost of emissions is considered into the valuation to tackle environmental issues. Given some simplifications in the plant cash-flow modelling, the value of such plant can either be expressed as the price of i) a cross-commodity option or ii) the price of a real option. Here, we focus on cross-commodity option valuation approach where the value of the power plant is approached as the value of a spark spread option. When spot prices of the underlying commodities are log-normal, closed formulae or approximations can be obtained using Kirk's approximation. Naturally, the spot price of electricity and gas present spikes due to seasonality among other factors. However, in that case it is not possible to get a closed formula for the spark spread option. In this paper we explore possibilities to approximate spark spread options when spot prices fall into a class of jump diffusion processes.