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Volume 8, Issue 5
Modeling and Computation of CO2 Allowance Derivatives Under Jump-Diffusion Processes

Shuhua Zhang & Jing Wang

DOI: 10.4208/aamm.2015.m1001

Adv. Appl. Math. Mech., 8 (2016), pp. 827-846.

Published online: 2018-05

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  • Abstract

In this paper, we study carbon emission trading whose market is gaining popularity as a policy instrument for global climate change. The mathematical model is presented for pricing options on $CO_2$ emission allowance futures with jump diffusion processes, and a so-called fitted finite volume method is proposed to solve the pricing model for the spatial discretization, in which the Crank-Nicolson is employed for time stepping. In addition, the stability and the convergence of the fully discrete scheme are given, and some numerical results, which are compared with the closed form solution and the Monte Carlo simulation solution, are provided to demonstrate the rates of convergence and the robustness of the numerical method.

  • Keywords

$CO_2$ emission allowance, option pricing, jump diffusion, fitted finite volume method, partial integro-differential equation, fast Fourier transform.

  • AMS Subject Headings

65M12, 65M60, 91B28

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-8-827, author = {Zhang , Shuhua and Wang , Jing}, title = {Modeling and Computation of CO2 Allowance Derivatives Under Jump-Diffusion Processes}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {8}, number = {5}, pages = {827--846}, abstract = {

In this paper, we study carbon emission trading whose market is gaining popularity as a policy instrument for global climate change. The mathematical model is presented for pricing options on $CO_2$ emission allowance futures with jump diffusion processes, and a so-called fitted finite volume method is proposed to solve the pricing model for the spatial discretization, in which the Crank-Nicolson is employed for time stepping. In addition, the stability and the convergence of the fully discrete scheme are given, and some numerical results, which are compared with the closed form solution and the Monte Carlo simulation solution, are provided to demonstrate the rates of convergence and the robustness of the numerical method.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1001}, url = {http://global-sci.org/intro/article_detail/aamm/12119.html} }
TY - JOUR T1 - Modeling and Computation of CO2 Allowance Derivatives Under Jump-Diffusion Processes AU - Zhang , Shuhua AU - Wang , Jing JO - Advances in Applied Mathematics and Mechanics VL - 5 SP - 827 EP - 846 PY - 2018 DA - 2018/05 SN - 8 DO - http://doi.org/10.4208/aamm.2015.m1001 UR - https://global-sci.org/intro/article_detail/aamm/12119.html KW - $CO_2$ emission allowance, option pricing, jump diffusion, fitted finite volume method, partial integro-differential equation, fast Fourier transform. AB -

In this paper, we study carbon emission trading whose market is gaining popularity as a policy instrument for global climate change. The mathematical model is presented for pricing options on $CO_2$ emission allowance futures with jump diffusion processes, and a so-called fitted finite volume method is proposed to solve the pricing model for the spatial discretization, in which the Crank-Nicolson is employed for time stepping. In addition, the stability and the convergence of the fully discrete scheme are given, and some numerical results, which are compared with the closed form solution and the Monte Carlo simulation solution, are provided to demonstrate the rates of convergence and the robustness of the numerical method.

Zhang , Shuhua and Wang , Jing. (2018). Modeling and Computation of CO2 Allowance Derivatives Under Jump-Diffusion Processes. Advances in Applied Mathematics and Mechanics. 8 (5). 827-846. doi:10.4208/aamm.2015.m1001
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