# American Institute of Mathematical Sciences

## Design of green bonds by double-barrier options

 1 Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China 2 College of Science, Tianjin University of Commerce, Tianjin 300134, China 3 Department of Mathematics and Statistics, Curtin University, Perth, WA6845, Australia

* Corresponding author: Zhuo Yang

Received  September 2018 Revised  October 2018 Published  September 2019

Fund Project: 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 (11771322), the Social Science Fund of Tianjin (TJYJ18023), and the Key Projects of Ministry of Education (DIA160334).

Green finance is an innovative model that can promote sustainable economic development. The green bonds also develop gradually as a part of green finance. The green bonds are designed to fund the projects of positive environmental impact. If the green bonds are superior to other debt securities, they will attract more investors' participation in green energy projects. Thus, the design of green bonds is crucial to the development of green bonds market. This article assumes that the floating rate of green bonds is linked to carbon price, and carbon price is described by a jump diffusion process. The carbon price fluctuation can lead to interest rate fluctuation of green bonds. We set two boundary values of carbon price, and the coupon rate is revalued when the carbon price reaches the boundary. The higher the carbon price is, the higher the coupon rate is to be paid by issuers. Thus, the boundary can impel issuers to boost energy savings and emission-reduction, and the higher interest rate will also attract more investors to invest in green bonds. The lower the carbon price is, the lower the interest rate is to be paid by issuers. Accordingly, the boundary may encourage issuers to boost emission reduction. This design can monitor and incentivize issuers to make more contribution to green finance. Furthermore, the design is characterized by the double-barrier option, such that the interest rate of green bonds can be obtained by double-barrier option pricing. Subsequently, the central difference method and the composite trapezoidal formula are employed to obtain the numerical solution. Finally, we conduct the sensitivity analysis of the model.

Citation: Shuhua Zhang, Zhuo Yang, Song Wang. Design of green bonds by double-barrier options. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020110
##### References:

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##### References:
Index-linked green bonds issued by World Bank
The carbon prices and its rates of return from 2012 to 2018
The green bond interest rates when it has no barriers and it has barriers
The green bond interest rates when the barrier changes in non barriers and barriers
The effects of parameters $r$ and ${\sigma}$ on the green bond interest rate
The effects of parameters ${\lambda}$ on the green bond interest rate
Parameters' values
 Parameters Values Parameters Values $r$ 0.019 $\delta$ 0.5 $\sigma$ 0.106 $\mu$ -0.06 $\lambda$ 0.04
 Parameters Values Parameters Values $r$ 0.019 $\delta$ 0.5 $\sigma$ 0.106 $\mu$ -0.06 $\lambda$ 0.04
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