基于GARCH-分形布朗运动模型的碳期权定价研究

Carbon option pricing based on fractional Brownian motion combined with GARCH model

文章将广义自回归条件异方差(generalized autoregressive conditional heteroskedasticity,GARCH)模型和分形布朗运动结合引入碳金融期权定价研究中。通过对欧洲碳排放配额(European Union Allowance,EUA)期货收盘价的样本数据检验,发现其存在尖峰厚尾、条件异方差性和分形特征;采用GARCH模型拟合并预测碳价收益率波动率;将预测的波动率作为输入值代入分形布朗运动期权定价方法,运用蒙特卡罗模拟对EUA期货期权进行定价,并与B-S期权定价法(Black-Scholes Option Pricing Model)比较。结果表明,基于GARCH分形布朗运动模型的碳期权定价法预测精度有显著提高。

This paper introduces the idea of combining generalized autoregressive conditional heteroskedasticity （GARCH） model and fractional Brownian motion into carbon option pricing. Firstly, the test results from closing wice of European Union Allowance（EUA） Futures show that obvious peak and fat tails, heteroscedasticity and fractal feature reside in the data. Secondly, the GARCH model is used to fit the volatility of EUA Futures price, which can reasonably describe and forecast the time-varying volatility. With the forecasted volatility being the input in fractional Brownian motion carbon option pricing, the Monte Carlo simulation is used to simulate the pricing of EUA Futures options, and then the pricing result is compared with that of Black-Scholes option pricing model. The result shows that carbon option pricing based on fractional Brownian motion combined with GARCH model can improve the pricing accuracy.