Option valuation using fast fourier transform in the carbon emissions market

Abstract

Kyoto Protocol is an international agreement which commits Annex 1 parties by setting international binding carbon emission reduction targets. Carbon emission trading involves the buying and selling of carbon allowances in the event of non-compliance with the emission reduction targets. There is a lot of price volatility in the carbon emissions market. Most traders use option derivatives to deal with the risks. The non-compliance event defines the price process of the carbon allowances. The non-compliance event is modelled using the normal inverse Gaussian distribution and Brownian motion. The carbon price data is fitted in NIG distribution and Brownian motion using MLE. This helps us know which distribution best fits our data set. The results suggest that normal inverse Gaussian model has a better than Brownian motion. A simple analytic expression for the Fourier transforms using NIG and Brownian motion characteristic functions is defined and used to solve the European time option prices. The results suggest that NIG gives a higher option price than Brownian motion.