Introducing carbon financial derivatives and improving the carbon trading system are indispensable means for promoting carbon emission reductions. However, the reasonable pricing of carbon financial derivatives is crucial for launching related financial products. Here, the bilateral gamma distribution was used to fit the carbon quota yield series for the first time and compute the volatility of the carbon quota price, based on which the carbon option price was calculated by optimizing the option pricing model. The experimental results show that the carbon quota yield sequence approximately follows the bilateral gamma distribution and the model is reasonable for carbon option pricing. Subsequently, considering the relationship between continuous rise and fall rate in yield and the influence of trading volume on price, the formula of conditional probability of price rise and fall is derived by using bilateral gamma distribution, and numerical verification is carried out. Therefore, bilateral gamma distribution can be used for option pricing and price probability inference in carbon trading.