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Probability and Computational Finance Seminar
Daniel Schwarz Carnegie Mellon University Title: Price Modelling in Carbon Emission and Electricity Markets Abstract: We present a model to explain the joint dynamics of the prices of electricity and carbon emission allowance certificates as a function of exogenously given fuel prices and power demand. The model for the electricity price consists of an explicit construction of the electricity supply curve; the model for the allowance price takes the form of a coupled forward-backward stochastic differential equation (FBSDE). Reflecting typical properties of emissions trading schemes the terminal condition of this FBSDE exhibits a gradient singularity. Appealing to compactness arguments we prove the existence of a unique solution to this equation and, using formal asymptotic arguments, we illustrate its connection to scalar valued conservation law partial differential equations.A possible application of such a model is the pricing of clean spread options, contracts that are frequently used to value power plants in the spirit of real option theory. Date: Monday, September 17, 2012 Time: 5:00 pm Location: Wean Hall 6423 Submitted by: Dmitry Kramkov |