The 1987 crash was a 27-sigma event under the log-normal model.

Evidence

There is little doubt which event separates the second and third phases: the stock market crash of October 1987, particularly Monday, October 19, 1987, when American stocks suffered their largest ever one-day fall. That day, the Standard and Poor’s (S&P) 500 index fell 20%, and the S&P 500 two-month future on the Chicago Mercantile Exchange—probably a better indicator because of trading disruptions in New York—fell 29% (Jackwerth and Rubinstein 1996, p. 1611). Qualitatively, the emergence of the skew is close to consistent with standard notions of rational learning. On the log-normal model, the fall in the S&P future price on that dreadful Monday was a 27j event; its probability was (Jackwerth and Rubinstein 1996, p. 1612). — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 142

The crash was a grotesquely unlikely event on the log-normal model of stock-price movements underpinning that theory. In terms of the log-normal model, the fall on October 19 of “the two month S&P 500 futures price … is a -27 standard deviation event with probability 10-160” (Jackwerth and Rubinstein 1996, pp. 1611-1612). — Donald MacKenzie, An Engine, Not a Camera, 845

Categorization

• SHARE: A 27-sigma event is a striking stat for anyone into quantitative finance - the ‘impossible’ crash that broke option pricing.
• CANDY: A fun conversation fact: the 1987 crash was mathematically near-impossible under the standard model, yet it happened.
• QUESTION: What exactly does a -27 standard deviation event imply about the adequacy of the log-normal model — and do alternative stochastic models fare any better?
• XREF: Connects to the performativity thesis and its counterperformativity failure modes introduced earlier in the book. — connects to: Implied volatility spiked from 20 to 170 percent in the 1987 crash. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 919; The 1987 crash was a multi-sigma event under the log-normal assumption. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 142
• corroborated: 2 independent passages support this claim — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 142; Donald MacKenzie, An Engine, Not a Camera: How Financial…, 845

Broader Connections

• Implied volatility spiked from 20 to 170 percent in the 1987 crash. #expands (0.85) — Donald MacKenzie, An Engine, Not a Camera, 919