Stability of the Numerical Schemes used for Pricing Green Bonds

Abstract

This master's thesis provides information on the subject of option pricing theory. Moreover, this topic is linked with sustainable Finance, which is essential in the battle against climate change. Green financing is a growing phenomenon, and a green bond is only a relatively new example of a green financial derivative. A three-dimensional PDE is at hand to determine the price of a green bond (also called a coupon value), but this PDE can only be solved numerically. This master thesis aims to determine the stability of certain numerical schemes that can be used to find a solution to the PDE. We will use both forward and backward differences to derive the numerical schemes. After the derivation process, a Von Neumann analysis is performed to conclude whether or not the schemes are stable. The research reveals that most of the numerical schemes are not stable. Amongst others, this is caused by the positive value of the interest rate $r$, the value of the carbon price, and the absence of damping factors. In some numerical schemes, the amplification factor is larger than one, but not by much. In other schemes, we can reduce the amplification factor to increase the stability. This means that the numerical schemes can still be used to find a reasonable value for a green bond.