Pricing green financial options under the mixed fractal Brownian motions with jump diffusion environment

Abstract

To cope with severe climate change, traditional emission reduction and environmental protection measures must be supported by financial instruments. The paper investigates green financial options, measured by the green cryptocurrency (Solana) and carbon emissions allowances, under fractal Brownian motions with jump detection. To this purpose, after observing the dynamic price correlations between all the variables. We introduce a mixed fractional Brownian motion model for the two types of green financial assets with possible jumps driven by an independent Poisson process. Then, pricing European green crypto options and carbon options in a generalized mixed fractional Brownian Motion with jumps detection. This research aims to explore the strategy of European contingent claims written on the underlying asset of green financial assets. When the underlying asset prices follow the mixed fractional Brownian motion with jumps the valuation of European call and put green financial options can be discovered. The finding provides a meaningful and enlightening reference to avoiding green investment risk. More generally, it could be beneficial for responsible investment and risk management in green financial markets under green financial regulations to protect investors and public interests.