In financial modeling problems, non-Gaussian tails exist widely in many circumstances. Among them, the accurate estimation of risk-neutral distribution (RND) from option prices is of great importance for researchers and practitioners. A precise RND can provide valuable information regarding the market's expectations, and can further help empirical asset pricing studies. This paper presents a parsimonious parametric approach to extract RNDs of underlying asset returns by using a generative machine learning model. The model incorporates the asymmetric heavy tails property of returns with a clever design. To calibrate the model, we design a Monte Carlo algorithm that has good capability with the assistance of modern machine learning computing tools. Numerically, the model fits Heston option prices well and captures the main shapes of implied volatility curves. Empirically, using S\&P 500 index option prices, we demonstrate that the model outperforms some popular parametric density methods under mean absolute error. Furthermore, the skewness and kurtosis of RNDs extracted by our model are consistent with intuitive expectations. More generally, the proposed methodology is widely applicable in data fitting and probabilistic forecasting.

翻译：在金融建模问题中，非高斯尾部广泛存在于诸多情境。其中，基于期权价格准确估计风险中性分布（RND）对研究人员及从业者具有重要意义。精确的RND既能揭示市场预期的关键信息，又能为实证资产定价研究提供支撑。本文提出一种简约参数化方法，通过生成式机器学习模型提取标的资产收益的RND。该模型通过精巧设计融入了收益的非对称厚尾特性。为校准模型，我们设计了蒙特卡洛算法，借助现代机器学习计算工具展现出良好性能。数值实验表明，该模型能有效拟合Heston期权价格并捕捉隐含波动率曲线的主要形态。基于标普500指数期权价格的实证结果显示，在平均绝对误差准则下，本模型优于若干主流参数密度方法。此外，模型提取的RND偏度与峰度均符合直观预期。更广泛而言，所提方法可普遍应用于数据拟合与概率预测领域。