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Singular Forward-Backward Stochastic Differential Equations and Emissions Derivatives

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  • Rene Carmona
  • Francois Delarue
  • Gilles-Edouard Espinosa
  • Nizar Touzi
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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.

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    File URL: http://arxiv.org/pdf/1210.5773
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    Paper provided by arXiv.org in its series Papers with number 1210.5773.

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    Date of creation: Oct 2012
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    Handle: RePEc:arx:papers:1210.5773

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    Web page: http://arxiv.org/

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    1. Marc Chesney & Luca Taschini, 2008. "The Endogenous Price Dynamics of the Emission Allowances: An Application to CO2 Option Pricing," Swiss Finance Institute Research Paper Series 08-01, Swiss Finance Institute, revised Jan 2008.
    2. Seifert, Jan & Uhrig-Homburg, Marliese & Wagner, Michael, 2008. "Dynamic behavior of CO2 spot prices," Journal of Environmental Economics and Management, Elsevier, vol. 56(2), pages 180-194, September.
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