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.

翻译：在金融建模问题中，非高斯尾部广泛存在于多种情形。其中，基于期权价格准确估计风险中性分布对研究者和从业者至关重要。精确的风险中性分布能够提供有关市场预期的宝贵信息，并进一步助力实证资产定价研究。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风险中性分布。该模型通过巧妙设计融入收益的非对称厚尾特性。为校准模型，我们设计了一种蒙特卡洛算法，借助现代机器学习计算工具具有良好的能力。数值实验表明，该模型能良好拟合赫斯顿期权价格，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分析显示，该模型在平均绝对误差指标上优于部分主流参数密度方法。此外，由本模型提取的风险中性分布的偏度和峰度与直觉预期一致。