Black and Scholes succeeded by proving their formula solved a theoretically justified differential equation

Evidence

Black and Scholes’s tinkering with the formula for the expected value of an option’s payoff was in one sense no different from what Boness or Thorp had done. However, Boness’s justification for his choice of expected rate of return on stock was empirical he chose “the rate of appreciation most consistent with market prices of puts and calls” (Boness 1964, p. 170) and Thorp freely admits that he “guessed” that the right thing to do was to set the stock’s rate of return equal to the riskless rate: it was “guesswork, not proof” (Thorp interview). Black and Scholes, on the other hand, could prove mathematically that their call option formula was a solution to their differential equation, and the latter had a clear theoretical, economic justification. — Donald MacKenzie, An Engine, Not a Camera, 584

Categorization

• XREF: Contrast between proof-based justification and guesswork echoes the broader performativity literature’s interest in how rigorous derivations confer authority on economic models, and connects to the empirical-vs-theoretical justification split seen in Milgrom’s institution work. — connects to: The arbitrage argument produces the Black-Scholes partial differential equation. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95; CAPM’s economic rationale licensed mathematically unrigorous stochastic calculus by Black and Scholes — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 586; Deriving the Black-Scholes equation required invoking CAPM’s riskless-rate logic. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 581 (+3 more)

Broader Connections

• Deriving the Black-Scholes equation required invoking CAPM’s riskless-rate logic. #expands (0.85) — Donald MacKenzie, An Engine, Not a Camera, 581