Trading in options with a wide range of exercise prices and a single maturity allows a researcher to extract the market's risk-neutral density (RND) over the underlying price at expiration. The RND contains investors’ beliefs about the true probabilities blended with their risk preferences, both of which are of great interest to academics and practitioners alike. With a particular focus on US equity options, I review the historical development of this powerful concept, practical details of fitting an RND to options market prices, and the many ways in which investigators have tried to distill true expectations and risk premia from observed RNDs. I briefly discuss areas of active current research including the pricing kernel puzzle and the volatility surface, and offer thoughts on what has been learned about RNDs so far and fruitful directions for future research.

中文翻译：

---

风险中性密度：回顾

以广泛的执行价格和单一到期日进行期权交易可以使研究人员在到期时从标的价格中提取市场的风险中性密度（RND）。RND包含投资者对真实概率的信念以及他们的风险偏好，这两者对于学者和从业者都非常感兴趣。我特别关注美国股票期权，回顾了这一强大概念的历史发展，使RND适合期权市场价格的实际细节，以及研究人员试图从观察到的RND中提取真实期望和风险溢价的多种方式。我简要讨论了当前活跃的研究领域，包括定价核心难题和波动表面，