Research On Carbon Option Pricing Based On GARCH And Fractal Brownian Motion

Since the 1990s,environmental pollution whice is mostly related to carbon emissions has attracted worldwide attention.The world has been working hard to reduce carbon emissions.As the world’s largest emitter of greenhouse gases,China participates in carbon trading actively,which has been expanded from pilot trading to national trading.Around the newly proposed "carbon peak and carbon neutral" goals,many provinces and cities across the country have started actions.At the same time,this puts forward higher requirements to China.However,since the main carbon trading market is abroad currently,China can only accept the low prices given by the carbon trading market passively.In order to improve its position in the carbon emissions trading market effectively,China needs to improve the carbon trading market further.Therefore,it is important to price carbon properly.The development of the carbon derivatives market and the spot market complement each other.Considering that the spot price formation mechanism in the international carbon emission market is relatively mature,pricing carbon options may be a breakthrough in China’s research.Based on this,this paper selects carbon options in the EU carbon trading market as a sample for pricing research,hoping to provide a reference for the establishment of China’s carbon options market.This paper takes the carbon option trading that needs to be developed urgently in China as an entry point,and analyzes the status quo of carbon emission trading and the influencing factors of carbon option prices based on fractal market theory,option pricing theory and other related theories systematically.According to the analysis results,this paper selects EUA option of the EU carbon emission trading market as the research sample to conduct descriptive statistical analysis of price series and other GARCH model family tests.The return volatility of carbon options has been proved to be conditional heteroscedasticity,and the construction of the GARCH model can fit the volatility of carbon options well.At the same time,the Hurst exponent value of the carbon option price series is about 0.32,which is different from 0.5 significantly,indicating that the price of carbon options conforms to the fractal Brownian motion(FBM).Therefore,it can be used to fit the actual price fluctuations of carbon options.On this basis,this paper constructs a pricing model based on GARCH and FBM to conduct pricing research on EUA carbon options.And determine the execution price,expiration date,any time,stock price,risk-free interest rate,volatility and Hurst exponent and other FBM parameter values respectively.From this,the carbon option price for the 60-day forecast period is calculated and compared with the actual price.The research results show that the prediction results of the option pricing model based on GARCH and FBM have a high degree of fitting to the actual price of carbon options,and the effect of predicting the price of carbon options can be achieved basically.To further evaluate the effect of the model.This paper uses three error evaluation indicators of MAPE,MAE and MSE to evaluate the error between the predicted price and the actual price of the four commonly used pricing models.The result proves that the error of this model is the smallest,which is better than the other three models significantly.There are two innovations in this study: First,use the FBM model to price carbon options.Second,construct the GARCH model to modify the volatility of FBM.Using the modified FBM model to study carbon option pricing will not only help enrich carbon option pricing theory and FBM model theory,but also provide a reference for China’s carbon option trading.At the same time,it provides a basis for enterprises to make scientific carbon investment decisions.