Black-Scholes assumes away the price gaps that would break its hedging strategy.

Evidence

“The analogy with insurance breaks down,” they warned, if stock prices “gapped” downward, plunging discontinuously: there would not be “sufficient time to adjust the replicating portfolio” (Rubinstein and Leland 1981, p. 72). Such discontinuities were excluded, mathematically, from the Black-Scholes log-normal random walk, but could not be ruled out in practice. — Donald MacKenzie, An Engine, Not a Camera, 805

Categorization

• DEFINE: Clarifies the key contrast between the Black-Scholes log-normal random walk (which excludes discontinuities) and real markets where price gaps occur — central to the performativity thesis.
• XREF: connects to: The Black-Scholes equation’s assumption of known underlying prices failed on NASDAQ’s dealer structure. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 130; Black-Scholes pricing rests on idealized no-friction market assumptions. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 627; Black-Scholes delta hedging fails when indices jump discontinuously or volatility spikes — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 924

Broader Connections

• Black-Scholes delta hedging fails when indices jump discontinuously or volatility spikes #expands (0.90) — Donald MacKenzie, An Engine, Not a Camera, 924