In this paper, we consider the response of the oil-futures option market to the onset of severe conditions in the aftermath of Feb. 15, 2020. Motivated in part by the decline of the WTI futures contract into negative territory on April 20, 2020, for the derivative market on oil futures we consider an analytical contrast between the traditional Black model and its long-ago predecessor, the Bachelier model. Under 2020 crash conditions, the Bachelier model performs better than Black, displaying a significantly flatter vol smile. Based in part on previous published research for short-dated maturities , the rationale for this difference is built on the contrast between between implied Black and Bachelier volatilities. Other than for extreme strikes and high Black vols, we show that the rapport works well in a wider range of maturities and volatilities. Using options data over the year 2020, we explore a notion of normalized strike to measure quantitatively the vol skew.

在本文中，我们考虑了石油期货期权市场对 2020 年 2 月 15 日之后出现的严峻形势的反应。部分原因是 WTI 期货合约在 2020 年 4 月 20 日跌至负值区域，对于石油期货的衍生品市场，我们考虑了传统 Black 模型与其很久以前的 Bachelier 模型之间的分析对比。在 2020 年的碰撞条件下，Bachelier 模型的表现优于 Black，显示出明显更平坦的微笑。部分基于先前发表的短期到期研究，这种差异的基本原理是建立在隐含的黑色和 Bachelier 波动率之间的对比之上。除了极端罢工和高黑色波动之外，我们表明这种融洽的关系在更广泛的期限和波动范围内运作良好。