Risk-neutral densities contain rich information about investors' risk averseness and expectations for the future. In this paper, we use the Bilateral Gamma model to fit the risk-neutral density because it provides more flexible tail behaviours than the widely used Variance Gamma model. A traditional model calibrating method uses numerical optimisation to minimize the sum of the distance between the market price and the model price. However, it suffers from local minima and is sensitive to the initial value used. Compared to numerical optimisation, the moment-matching method is more time-efficient but shows less accuracy than numerical optimisation. Motivated by this, we combine the moment-matching method and numerical optimisation to balance time-consuming and model performance.
