Fitted finite volume method for pricing CO₂ futures option based on the underlying with non-log-normal distribution

Abstract

By analysing spot price characteristics at compliance time from equilibrium perspective, the CO${}_2$ price dynamical models are obtained for both bankable and nonbankable regulations with the prices of spots and futures being non-log-normal, and the futures option pricing model is established. Then, a fitted finite volume method (FVM) is proposed to solve the pricing model. Also, its monotonicity, stability, and convergence are studied. Furthermore, the convergence rates are compared between our fitted FVM and the finite difference method. Moreover, the Δ-hedge experiments are performed, in which the hedge cost and the hedge error are estimated. Finally, using the Monte Carlo's pricing results as a benchmark, we compare the computational results from the fitted FVM and the Black formula approximation, respectively, which shows that the former is fitted for the Monte Carlo better than the latter, especially for the futures options with the bigger volatility or the maturity near the compliance time.

Keywords:

• CO${}_2$ emission allowance
• compliance time
• option pricing
• non-log-normal distribution
• finite volume method

2010 AMS Subject Classifications:

• 65M08
• 91B76
• 91G20
• 91G80

Disclosure statement

No potential conflict of interest was reported by the authors.

Funding

This project was supported in part by the National Basic Research Program [2012CB955804], the Major Research Plan of the National Natural Science Foundation of China [91430108], the National Natural Science Foundation of China [11171251, 11201111], and the Major Program of Tianjin University of Finance and Economics [ZD1302].