In the face of severe climate change, researchers have looked for assistance from financial instruments. They have examined how to hedge the risks of these instruments created by market fluctuations through various green financial derivatives, including green bonds (i.e., fixed-income financial instruments designed to support an environmental goal). In this study, we designed a green bond index option contract. First, we combined an autoregressive moving-average model (AMRA) with a generalized autoregressive conditional heteroskedasticity model (GARCH) to predict the green bond index. Next, we established a fractional Brownian motion option pricing model with temporally variable volatility. We used this approach to predict the closing price of the China Bond–Green Bond Index from 3 January 2017 to 30 December 2021 as an empirical analysis. The trend of the index predicted by the ARMA–GARCH model was consistent with the actual trend and predictions of actual prices were highly accurate. The modified fractional Brownian motion option pricing model improved the pricing accuracy. Our results provide a policy reference for the development of a green financial derivatives market, and can accelerate the transformation of markets towards a more sustainable economic development model.