Pricing of American Carbon Emission Derivatives and Numerical Method under the Mixed Fractional Brownian Motion

Abstract

This paper studies the pricing of American carbon emission derivatives and its numerical method under the mixed fractional Brownian motion. To capture the long memory properties such as self-similarity and long-range dependence in the price process, we proposed a model based on a fractional Black–Scholes, which is more in line with the actual characteristics of the option market. We have outlined a power penalty approach using parabolic variation inequality and linear complementarity (LCP) which arises from mixed fractional Brownian motion. In addition, we introduced a nonuniform grid-based modification of the fitted finite volume method for numerical solution. Numerically, we show the impact of Hurst exponent on the pricing and analyze the convergence rates of the proposed penalty method. In conclusion, since mfBm is a well-developed mathematical model of strongly correlated stochastic processes, this model will be an efficient model for pricing carbon financial derivative.