25/09/2013, 11:00 — 12:00 — Room P3.10, Mathematics Building Daniel Schwarz, IST and CMU

Price Modelling in Carbon Emission and Electricity Markets

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) with random coefficients.
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. We illustrate the relevance of
the model at the example of pricing clean spread options, contracts
that are frequently used to value power plants in the spirit of
real option theory.