Maguolo, Gianluca (2017) Risk-Neutral Pricing of Emission Related Derivatives: a Numerical Solution. [Magistrali biennali]
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We introduce the problem of pricing emission allowances introducing one basic model from which we obtain a forward-backward stochastic differential equation (FBSDE) with a discontinuous terminal condition. We show that, under some conditions on the forward component, the solution of the equation exists and is unique. Then we solve the equation using a relation between the solution of the FBSDE and the solution of a quasi-linear partial differential equation that we are able to compute numerically. Finally, we apply the numerical method to a simple model that considers delay in the information.
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