Abstract: This paper designs a new training algorithm which fuses parameter models and nonparameter models. By using the machine learning model to simulate parameter models as prior distribution, optimizing it with Bayesian learning, and dynamically adjusting distribution, this algorithm can avoid the excessive volatility of mode parameters and increase the generation ability. Based on the BS model (Black Scholes option pricing model), the Heston model, and neural network, this paper constructs the fusion modes of BS_BR and HS_BR for option pricing. The result of the empirical study shows that the fusion model can combine the advantages of the two modes, which has not only a better calibration efficiency in the sample, but also a better prediction performance out of the sample.

Key words: machine learning, option pricing, parameter model, neural network, Bayesian learning

摘要： 设计了融合参数模型和非参数机器学习模型进行训练的算法，利用非参数模型拟合参数模型，将其作为先验分布，然后采用贝叶斯学习方法进行优化，并在训练中实现分布的动态调整。该方法在训练过程中有助于避免模型参数过度波动，提升模型泛化能力。针对期权定价，在BS、Heston等参数模型及神经网络等机器学习模型基础上，构建了相应的融合模型BS_BR和HS_BR，并利用市场数据进行了实证分析。研究表明，融合模型可以较好地发挥两类模型的优势，无论是在样本内拟合效率，还是样本外预测能力方面都具有更好的表现。

关键词: 机器学习, 期权定价, 参数模型, 神经网络, 贝叶斯学习