This thesis presents a novel approach to the pricing of green bonds, a growing segment in financial markets with an emphasis on environmental sustainability. Unlike traditional financial instruments, green bonds uniquely incorporate environmental considerations, particularly carbon price (c_t), along with traditional factors like the short rate (r_t), into their valuation. This integration is increasingly relevant in today’s economy, reflecting a shift towards sustainable finance. The core of this research involves applying advanced numerical methods, including the Finite Difference Method, Crank-Nicolson discretization, GMRES and Bi-CGSTAB, in order to develop and analyze pricing models for both green and conventional bonds. The study aims to assess how environmental factors impact the efficiency of these numerical techniques and to compare the outcomes with conventional bond models. The research reveals that green bonds, compared to conventional bonds, present unique numerical challenges, notably requiring more iterations for convergence in iterative methods GMRES and Bi-CGSTAB because of the high carbon price volatility (σc) and the ’Greenium’ phenomenon. Moreover, the comparative analysis showed that while Bi-CGSTAB outperforms GMRES in the green bond model, the opposite is true for conventional bonds. This study not only contributes to the theoretical understanding of green bond pricing but also offers practical insights for financial analysts and investors navigating this evolving market.

Keywords: Green Bonds, Bond Pricing, Zero-Coupon Bond, Short Rate Modeling, Numerical Methods, Crank-Nicolson, GMRES, BiCGSTAB, Environmental Finance, Sustainable Investing, Comparative Analysis, Financial Modeling.

In this report we investigate the spread of the coronavirus 2019 (COVID-19) using mathematical models. We start with a simplified model consisting of a system of three ordinary differential equations and expand it more and more to try to simulate reality. We use Python’s odeint function to solve these systems numerically. Because a fraction of all infected people will not develop any symptoms, it makes it easy for a virus to spread. Therefore we look at how big the effect asymptomatic people have on spreading the virus. We look at how government measures affect the spread of the virus and thereafter we look at what happens if the government eases the taken measures. We also use MATLAB to analyse the stability of our models and to find solutions to our models using different numerical methods.