CAPM’s economic rationale licensed mathematically unrigorous stochastic calculus by Black and Scholes

Evidence

Neither Black nor Scholes knew the mathematical theory needed to do calculus rigorously in a stochastic environment, but the Capital Asset Pricing Model provided an economic justification for what might otherwise have seemed dangerously unrigorous mathematics. “We did not know whether our formulation was exact,” says Scholes, “but intuitively we thought investors could diversify away any residual risk that was left.” — Donald MacKenzie, An Engine, Not a Camera, 586

Categorization

• SHARE: Worth sending to someone studying the sociology of scientific rigor: an elegant case of an economic theory justifying what the mathematicians themselves knew was formally shaky.
• QUESTION: Interesting whether Merton’s mathematically rigorous derivation later retroactively legitimated Black-Scholes in the eyes of the field, beyond the economic rationale.
• XREF: connects to: Merton’s stochastic calculus reframed derivatives pricing in terms of martingale theory — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 143; Deriving the Black-Scholes equation required invoking CAPM’s riskless-rate logic. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 581; Black and Scholes succeeded by proving their formula solved a theoretically justified differential equation — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 584 (+1 more)

Broader Connections

• Black and Scholes succeeded by proving their formula solved a theoretically justified differential equation #contradicts (0.85) — Donald MacKenzie, An Engine, Not a Camera, 584
• The arbitrage argument produces the Black-Scholes partial differential equation. #expands (0.80) — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95