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Singular forward-backward stochastic differential equations and emissions derivatives

Author(s): Carmona, Rene; Delarue, F; Espinosa, GE; Touzi, N

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Abstract: We introduce two simple models of forward-backward stochastic differential equations with a singular terminal condition and we explain how and why they appear naturally as models for the valuation of CO2 emission allowances. Single phase cap-and-trade schemes lead readily to terminal conditions given by indicator functions of the forward component, and using fine partial differential equations estimates, we show that the existence theory of these equations, as well as the properties of the candidates for solution, depend strongly upon the characteristics of the forward dynamics. Finally, we give a first order Taylor expansion and show how to numerically calibrate some of these models for the purpose of CO2 option pricing. © 2013 Institute of Mathematical Statistics.
Publication Date: 1-Jun-2013
Citation: Carmona, R, Delarue, F, Espinosa, GE, Touzi, N. (2013). Singular forward-backward stochastic differential equations and emissions derivatives. Annals of Applied Probability, 23 (3), 1086 - 1128. doi:10.1214/12-AAP865
DOI: doi:10.1214/12-AAP865
ISSN: 1050-5164
Pages: 1086 - 1128
Type of Material: Journal Article
Journal/Proceeding Title: Annals of Applied Probability
Version: Author's manuscript

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