Mathematics analyzes numerous aspects of financial markets and financial instruments. For the markets trading CO2 emissions (direct or the CO2 equivalent for other greenhouse gases), mathematics is used to decide how cap-and-trade rules will operate. The cap-and-trade mechanism sets future caps for pollution emissions and issues emission rights that can be bought and sold by the companies concerned. Producers that overstep their allotted cap must pay a penalty. Designing a market involves deciding in particular on a timetable for using permits, the initial mode of distribution (e.g., free attribution, bidding system, etc.), and how penalties operate.
These trading markets are still in their early stages. Under the impetus of the Kyoto protocol and its extension, a few attempts have been made to open up markets in some countries, beginning with the European Community in 2005 and followed by more recent initiatives in Australia, China and some American states.
Emissions trading provides a financial incentive to reduce greenhouse gas emissions from some sectors of economic activity. From theory to practice, mathematics can help obtain a clearer view of design choices so that setting up emissions trading can lead to effective reduction. Emissions trading also affects the price of goods, because greenhouse gas emissions are an externality of production, as well as the price of raw materials.
Game theory can be used to analyze interaction between stakeholders in these markets and to understand the connection between the design of cap and trade, the prices set for commodities such as electricity, windfall effects, and favored production technologies.
In addition, industrial production models can be used by a stakeholder subject to CO2 penalties. For a fixed market design, digital simulation can be used to quantify the stakeholder’s activity balance sheet (i.e., wealth produced, CO2 discharged) and calculate its subjective price to acquire a permit. Using this information, different designs can be tested and compared in line with varied criteria, including emissions reduction.
For more information:
“Carbon Value project: a quantitative study of short-term carbon value” with INRIA and MINES ParisTech.
Mireille Bossy (Inria Sophia Antipolis)
Nadia Maïzi (MinesParisTech Sophia Antipolis)
Odile Pourtallier (Inria Sophia Antipolis)