Option prices equal the cost of a portfolio that replicates the option’s payoff

Evidence

In contrast, Black, Scholes, and Merton’s arguments were at their core simple and elegant. If the price of a stock followed the standard model of a lognormal random walk in continuous time, and other simplifying assumptions held (see below), it was possible to hedge any option transaction perfectly. In other words, it was possible to construct a continuously adjusted portfolio of the underlying stock and government bonds or cash that would “replicate” the option: that would have the same return as it under all possible states of the world. Black, Scholes, and Merton then reasoned that the price of the option must equal the cost of the replicating portfolio: if their prices diverged, arbitrageurs would buy the cheaper and short sell the dearer, and this would drive their prices together. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95

Categorization

• DEFINE: Explains the core replication-and-no-arbitrage logic behind the Black-Scholes equation.
• XREF: connects to: Option price must equal the cost of a continuously adjusted replicating portfolio. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95; Option prices equal the expected payoff discounted at the riskless rate — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1284; Pricing under a risk-neutrality fiction yields the same option price as arbitrage pricing. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1283 (+2 more)

Related

• Option price must equal the cost of a continuously adjusted replicating portfolio. (similarity 0.95)
• Pricing under a risk-neutrality fiction yields the same option price as arbitrage pricing. (similarity 0.89)
• Option prices are set entirely by arbitrage, independent of risk attitudes or probabilities (similarity 0.88)
• The arbitrage argument produces the Black-Scholes partial differential equation. (similarity 0.87)
• The option price is independent of the stock’s expected return. (similarity 0.86)
• Risk-neutral valuation yields the identical option price as arbitrage arguments (similarity 0.85)
• the risk-neutral valuation insight lets options be priced by discounting at the riskless rate (similarity 0.85)
• Modern options pricing derives from arbitrage logic, not directional beliefs. (similarity 0.85)
• Black-Scholes legitimized options despite fitting prices only approximately (similarity 0.84)
• The Black-Scholes model reduces to a known physics equation solvable by hand (similarity 0.83)
• Derivative prices equal discounted expected payoffs under an equivalent martingale measure (similarity 0.82)
• Thorp independently derived a formula equivalent to Black-Scholes minus discounting. (similarity 0.82)
• The Black-Scholes formula contains no risk parameter, implying risk-neutral pricing. (similarity 0.82)
• The Black-Scholes equation excludes expected returns and risk aversion entirely (similarity 0.82)
• Continuous trading makes the hedged portfolio riskless, anchoring it to the riskless rate. (similarity 0.82)

Broader Connections

• Option price must equal the cost of a continuously adjusted replicating portfolio. #corroborates (1.00) — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95
• Option prices equal the expected payoff discounted at the riskless rate #corroborates (0.80) — Donald MacKenzie, An Engine, Not a Camera, 1284
• Derivative prices equal discounted expected payoffs under an equivalent martingale measure #corroborates (0.80) — Donald MacKenzie, An Engine, Not a Camera, 621
• Pricing under a risk-neutrality fiction yields the same option price as arbitrage pricing. #corroborates (0.75) — Donald MacKenzie, An Engine, Not a Camera, 1283
• Risk-neutral valuation yields the identical option price as arbitrage arguments #corroborates (0.75) — Donald MacKenzie, An Engine, Not a Camera, 1285