The arbitrage argument produces the Black-Scholes partial differential equation.

Evidence

This reasoning led to the famous Black-Scholes equation, where w is the price of the option, x the price of the stock, t time, j the volatility of the stock, and r the riskless rate of interest: 2 w 1 w w 2 2 j x rx rw p 0. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95

Categorization

• DEFINE: Locates the equation as the formal endpoint of the replicating-portfolio reasoning chain.
• 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; Arbitrage enforces a real link that anchors derivatives to underlying assets — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 781; Black and Scholes succeeded by proving their formula solved a theoretically justified differential equation — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 584 (+15 more)

Related

• Option prices equal the cost of a portfolio that replicates the option’s payoff (similarity 0.87)
• Deriving the Black-Scholes equation required invoking CAPM’s riskless-rate logic. (similarity 0.87)
• The Black-Scholes model reduces to a known physics equation solvable by hand (similarity 0.86)
• Finance theory treats arbitrage as enforcing equal risk-adjusted returns (similarity 0.85)
• Black and Scholes succeeded by proving their formula solved a theoretically justified differential equation (similarity 0.85)
• Arbitrage enforces a real link that anchors derivatives to underlying assets (similarity 0.84)
• Option price must equal the cost of a continuously adjusted replicating portfolio. (similarity 0.84)
• The Black-Scholes equation excludes expected returns and risk aversion entirely (similarity 0.84)
• Option prices are set entirely by arbitrage, independent of risk attitudes or probabilities (similarity 0.84)
• Black’s original derivation assumed CAPM pricing of both stock and warrant (similarity 0.83)
• Thorp independently derived a formula equivalent to Black-Scholes minus discounting. (similarity 0.83)
• Constrained arbitrage allows finance-theory models to diverge from actual prices. (similarity 0.83)
• Pre-Black-Scholes option models relied on unmeasurable parameters (similarity 0.83)
• CAPM’s economic rationale licensed mathematically unrigorous stochastic calculus by Black and Scholes (similarity 0.83)
• Market arbitrage requires only that investors prefer more wealth to less, not risk preferences (similarity 0.83)

Broader Connections

• Deriving the Black-Scholes equation required invoking CAPM’s riskless-rate logic. #qualifies (0.85) — Donald MacKenzie, An Engine, Not a Camera, 581
• Arbitrage enforces a real link that anchors derivatives to underlying assets #expands (0.82) — Donald MacKenzie, An Engine, Not a Camera, 781
• Black and Scholes succeeded by proving their formula solved a theoretically justified differential equation #expands (0.80) — Donald MacKenzie, An Engine, Not a Camera, 584
• Finance theory treats arbitrage as enforcing equal risk-adjusted returns #expands (0.75) — Donald MacKenzie, An Engine, Not a Camera, 1003