# On the Stochastic Properties of Carbon Futures Prices

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## Abstract

Pricing carbon is a central concern in environmental economics, due to the worldwide importance of emissions trading schemes to regulate pollution. This paper documents the presence of small and large jumps in the stochastic process of the CO\(_2\) futures price. The large jumps have a discrete origin, i.e. they can arise from various demand factors or institutional decisions on the tradable permits market. Contrary to the existing literature, we show that the stochastic process of carbon futures prices does not contain a continuous component (Brownian motion). The results are derived by using high-frequency data in the activity signature function framework (Todorov and Tauchen in J Econom 154:125–138, 2010; Todorov and Tauchen in J Bus Econ Stat 29:356–371, 2011). The implication is that the carbon futures price should be modeled as an appropriately sampled, centered Lévy or Poisson process. The pure-jump behavior of the carbon price might be explained by the lower volume of trades on this allowance market (compared to other highly liquid financial markets).

## Keywords

Carbon price Stochastic modeling Activity signature function## JEL Classification

C14 C32 G1 Q4## Notes

### Acknowledgments

We wish to thank the Editor Michael Finus as well as two anonymous referees for their advice, which led to a greatly improved version of the paper. Helpful comments were received from seminar participants at the 10th Envecon Applied Environmental Economics Conference in London (UKNEE). We wish to thank ECX for providing the data. The usual disclaimer applies.

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