Option Pricing Research On Carbon Financial Assets Based On Fractal Theory

In recent years, the increasingly severe global environmental problems have already become the restrictive factors for sustainable development of economy and society. Trade of carbon finance,as an effective way to coordinate the relation between environmental protection and economic growth, not only helps to drive down the carbon emissions but also boosts the global economic growth. As an important derivative financial instrument, trade of carbon options can improve the function of price discovering, which contributes to avoid the risk of carbon trading in the market and increases the liquidity of that. Therefore, it will promote the healthy development of the carbon market and help investors make rational investment decisions to do some research on the option pricing of carbon finance.At first, this paper theoretically explores the influences on the prices of carbon financial asset. Due to several factors like supply and demand, weather conditions, energy prices, macroeconomic situation and the quota policy, the closing prices of EUA futures which were due in December 2014, from April 9, 2013 to April 17,2014, have an obvious peak and fat-tail characteristic, heteroscedasticity, and fractal feature. Besides, according to B-S option pricing method, the assumption that prices of assets in carbon market follow random walk and returns are normally distributed does not match the price distribution of carbon financial assets. Hence, based on the fractional Brownian motion combined with GARCH model that does not require the assumption mentioned above and can describe the actual characteristics and long memory of carbon prices, this paper sets prices on carbon assets through a comprehensive study of the characters of the yields sequence. The results of empirical analysis show that AR(2)-GARCH(1,1) model can better describe the heteroscedasticity of the yield data, and in terms of the pricing accuracy, it is also superior to the other methods, such as the fractal Brownian motion option pricing method based on the historical volatility, B-S option pricing method based on that or GARCH model.The contributions of this dissertation are to expand the carbon option pricing method and provide theoretical basis and practice reference for investors and the upcoming carbon options trading in China.