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We introduce two simple models of forward-backward stochastic differentialequations with a singular terminal condition and we explain how and why theyappear naturally as models for the valuation of CO2 emission allowances. Singlephase cap-and-trade schemes lead readily to terminal conditions given byindicator functions of the forward component, and using fine partialdifferential equations estimates, we show that the existence theory of theseequations, as well as the properties of the candidates for solution, dependstrongly upon the characteristics of the forward dynamics. Finally, we give afirst order Taylor expansion and show how to numerically calibrate some ofthese models for the purpose of CO2 option pricing.

Singular Forward-Backward Stochastic Differential Equations and Emissions Derivatives