Risk Management in Commodity Markets: From Shipping to Agriculturals and Energy

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Spark Spread Options when Commodity Prices are Represented as Time Changed Processes

Elisa Luciano

Spark spread options are defined on the difference between the price of electricity and the price of the fuel used to generate it, usually natural gas. Being output-minus-input spread options, they approximate the cost of converting gas into electricity. They are not only used as hedging tools, but also play a key role in power plant valuation: they represent by far the most important correlation product in the energy context. Their pricing relies on the ability to model not only the single underlying processes, but also their dependence, and therefore their joint dynamics.

At the marginal level, it is well known that commodities, energy in particular, have trajectorial and statistical properties much more complex – or with greater deviations from normal returns – than some other assets. Return models able to describe skewness, kurtosis, and other deviations from normality have been proposed during the last decade, not only for commodities, but also – or, a fortiori – for energy. Lévy models, which include diffusive Brownian motion on the one hand, pure jump processes on the other, by now seem to be the general environment in which commodity processes for the 21st century can be studied. However, not all Lévy models seem to be able to capture the observed features of market prices and returns. The interest of the research community has been attracted by non diffusive, pure jump ...