The Black-Scholes formula contains no risk parameter, implying risk-neutral pricing.

Evidence

In a letter, Merton (1972b) told Fischer Black: “I … do not understand your reluctance to accept that the standard form of CAPM just does not work.” “What I sort of argued with them [Black and Scholes],” says Merton, “was, if it depended on the [capital] asset pricing model, why is it when you look at the final formula [equation 1 in appendix D] nothing about risk appears at all? In fact, it’s perfectly consistent with a risk-neutral world.” — Donald MacKenzie, An Engine, Not a Camera, 598

Categorization

• QUESTION: Why does a formula derived from an asset-pricing model that centers risk end up containing no risk term at all? This is the puzzle that drives the risk-neutral valuation revolution — worth chasing further into the derivation.
• XREF: Links to later derivative-valuation literature and to the idea that the formula’s independence from risk parameters is what makes it so easily performative in practice. — connects to: Unobservable volatility means the Black-Scholes-Merton model has no unique predicted price. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 102; The Black-Scholes equation excludes expected returns and risk aversion entirely — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 610; Black-Scholes pricing rests on idealized no-friction market assumptions. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 627 (+2 more)

Broader Connections

• The Black-Scholes equation excludes expected returns and risk aversion entirely #corroborates (1.00) — Donald MacKenzie, An Engine, Not a Camera, 610
• Black-Scholes pricing rests on idealized no-friction market assumptions. #expands (0.80) — Donald MacKenzie, An Engine, Not a Camera, 627
• Finance theory’s core models assume frictionless markets with no transaction costs or short-selling penalties #complicates (0.70) — Donald MacKenzie, An Engine, Not a Camera, 51
• Realistically, no unaided human could calculate a Black-Scholes option price by hand #complicates (0.70) — Donald MacKenzie, An Engine, Not a Camera, 712