The analysis of option pricing in derivative markets has commonly relied on the Black-Scholes model. This paper presents a conceptual and empirical analysis of option pricing with a focus on the validity of key assumptions embedded in the Black-Scholes model. Going beyond questioning the lognormality assumption, we investigate the role played by two assumptions made about the nature of price dynamics: quantile-specific departures from a unit root process, and the role of quantile-specific drift. Our analysis relies on a Quantile Autoregression (QAR) model that provides a flexible representation of the price distribution and its dynamics. Applied to the soybean futures market, we examine the validity of assumptions made in the Black-Scholes model along with their implications for option pricing. We document that price dynamics involve different responses in the tails of the distribution: overreaction and local instability in the upper tail, and underreaction in the lower tail. Investigating the implications of our QAR analysis for option pricing, we find that failing to capture local instability in the upper tail is more serious than failing to capture “fat tails” in the price distribution. We also find that the most serious problem with the Black-Scholes model arises in its representation of price dynamics in the lower tail.

衍生品市场期权定价的分析通常依赖于布莱克-斯科尔斯模型。本文对期权定价进行了概念和实证分析，重点关注布莱克-斯科尔斯模型中关键假设的有效性。除了质疑对数正态性假设之外，我们还研究了关于价格动态性质的两个假设所发挥的作用：单位根过程的分位数特定偏离以及分位数特定漂移的作用。我们的分析依赖于分位数自回归 (QAR) 模型，该模型提供价格分布及其动态的灵活表示。应用于大豆期货市场，我们检验了布莱克-斯科尔斯模型中假设的有效性及其对期权定价的影响。我们记录了价格动态涉及分布尾部的不同反应：上尾部反应过度和局部不稳定，下尾部反应不足。通过研究 QAR 分析对期权定价的影响，我们发现未能捕捉到上尾部的局部不稳定性比未能捕捉到价格分布中的“肥尾”更为严重。我们还发现 Black-Scholes 模型最严重的问题在于其对下尾价格动态的表示。