Reduced form modeling of emission derivatives using Levy processes.

Abstract

The European Trading Scheme (ETS) has been implemented as a way of reducing emissions of greenhouse gasses. In this scheme European Union emission allowances (EUAs) are traded during the so called trading period. In the end of the period, producers that have emitted more than what is covered by their allowances has to pay a fine in proportion the excessive emissions.

This thesis is concerned with modeling the price of derivatives on these allowances, specifically futures contracts and standard European options on these. In this thesis, a reduced-form approach based on the work of Carmona et al. [5] is taken. The the underlying for the futures price is the total emission in the market. This is modeled directly as a Levy process in this thesis.

The technique proposed in [7] is used to express the futures prices as an integral expression involving the characteristic function of the underlying process. This price is numerically approximated for some example models of the underlying.

The price for European calls is not expressed explicitly, but a method for numerical approximation is suggested. Furthermore, upper and lower bounds are found for the expected payoff. In the special case when the option has maturity at the end of the trading period, the expected payoff and the probability of payoff, is expressed analytically.