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.
Publisher
University of Nairobi