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June 2013 Singular forward–backward stochastic differential equations and emissions derivatives
René Carmona, François Delarue, Gilles-Edouard Espinosa, Nizar Touzi
Ann. Appl. Probab. 23(3): 1086-1128 (June 2013). DOI: 10.1214/12-AAP865


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 CO${}_{2}$ 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 CO${}_{2}$ option pricing.


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René Carmona. François Delarue. Gilles-Edouard Espinosa. Nizar Touzi. "Singular forward–backward stochastic differential equations and emissions derivatives." Ann. Appl. Probab. 23 (3) 1086 - 1128, June 2013.


Published: June 2013
First available in Project Euclid: 7 March 2013

zbMATH: 1276.60070
MathSciNet: MR3076679
Digital Object Identifier: 10.1214/12-AAP865

Primary: 60H30 , 91G80

Keywords: emissions derivatives , forward–backward stochastic differential equations , Stochastic analysis

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.23 • No. 3 • June 2013
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