Deriving the Black-Scholes equation required invoking CAPM’s riskless-rate logic.

Evidence

The risk of the hedged portfolio was, therefore, the kind of risk that could be diversified away. Therefore, according to the Capital Asset Pricing Model, the hedged portfolio could earn only the riskless rate of interest. With the expected return on the hedged portfolio known, simple manipulation led to a finite difference equation that could be transformed into a differential equation (again, equation 1 in appendix D), the Black-Scholes option-pricing equation, as it was soon to be called. — Donald MacKenzie, An Engine, Not a Camera, 581

Categorization

• XREF: Chain link: CAPM (the prior pricing theory) was a necessary premise in deriving Black-Scholes. Connects to the performativity theme of models building on models. — connects to: The arbitrage argument produces the Black-Scholes partial differential equation. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95; Black and Scholes priced options via CAPM while Thorp sought arbitrage without it — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 141; Thorp independently derived a formula equivalent to Black-Scholes minus discounting. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 558 (+5 more)

Broader Connections

• CAPM’s economic rationale licensed mathematically unrigorous stochastic calculus by Black and Scholes #corroborates (0.92) — Donald MacKenzie, An Engine, Not a Camera, 586