title: Modelling and computation in the valuation of carbon derivatives with stochastic convenience yields.
abstract: The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results.
authors.affiliation: Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China; Institute of Policy and Management, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Shuhua
authors.initials: S
authors.lastname: Chang
authors.affiliation: Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China.
authors.forename: Xinyu
authors.initials: X
authors.lastname: Wang
mesh_terms: D002245:Carbon Dioxide / Q000737:chemistry*; D002980:Climate; D057231:Climate Change; D003132:Commerce / Q000706:statistics & numerical data*; D003198:Computer Simulation; D004784:Environmental Monitoring; D017752:Greenhouse Effect / Q000191:economics* / Q000517:prevention & control; D006801:Humans; D007391:International Cooperation; D015233:Models, Statistical; D013269:Stochastic Processes
chemical_list: D002245:Carbon Dioxide