Black’s original derivation assumed CAPM pricing of both stock and warrant

Evidence

Black then assumed that the Capital Asset Pricing Model applied both to the stock and warrant, so that E(Ax) and E(Aw) would depend on, respectively, the beta of the stock and the beta of the warrant. He also assumed that the stock price followed a log-normal random walk and that he could eliminate those terms that are “second order” in At. In addition, Black seems to have simplified the problem by assuming that, as he and Scholes put it (1973, p. 640): “The stock pays no dividends or other distributions.” — Donald MacKenzie, An Engine, Not a Camera, 1266

Categorization

• XREF: connects to: Deriving the Black-Scholes equation required invoking CAPM’s riskless-rate logic. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 581; The Black-Scholes derivation descends directly from a corrected Treynor equation — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 569; Black and Scholes priced options via CAPM while Thorp sought arbitrage without it — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 141 (+1 more)

Broader Connections

• Black and Scholes priced options via CAPM while Thorp sought arbitrage without it #expands (0.88) — Donald MacKenzie, An Engine, Not a Camera, 141
• Deriving the Black-Scholes equation required invoking CAPM’s riskless-rate logic. #corroborates (0.82) — Donald MacKenzie, An Engine, Not a Camera, 581
• The Black-Scholes derivation descends directly from a corrected Treynor equation #expands (0.75) — Donald MacKenzie, An Engine, Not a Camera, 569
• The arbitrage argument produces the Black-Scholes partial differential equation. #qualifies (0.72) — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95