Black-Scholes delta hedging fails when indices jump discontinuously or volatility spikes

Evidence

Furthermore, to hedge index options by using the Black-Scholes “delta hedging” procedure (outlined in chapters 5 and 6) might well be insufficient if an index fell sharply: it might not be possible to adjust the hedge fast enough. In a Black-Scholes world there are no “jumps” no discontinuous price movements and no changes in volatility. 1987, however, taught options market makers that indices could go down effectively discontinuously while volatility could leap upward. If that happened, “delta hedging” would fail adequately to protect a market maker who had sold puts. — Donald MacKenzie, An Engine, Not a Camera, 924

Categorization

• DEFINE: Clarifies the model-world assumptions (no jumps, constant volatility) that delta hedging presupposes, and why 1987 violated them.
• XREF: Directly ties to the performativity thesis: the Black-Scholes model worked partly because market conditions roughly matched its assumptions; 1987 exposed the gap between model world and market world. — connects to: Black-Scholes assumes away the price gaps that would break its hedging strategy. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 805; Convertible bonds traded at prices inconsistent with Black-Scholes option valuations — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 967; Index option prices embed a skew that actual price movements do not justify — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 911 (+1 more)

Broader Connections

• Index option prices embed a skew that actual price movements do not justify #exemplifies (0.85) — Donald MacKenzie, An Engine, Not a Camera, 911
• Convertible bonds traded at prices inconsistent with Black-Scholes option valuations #expands (0.75) — Donald MacKenzie, An Engine, Not a Camera, 967