Option price must equal the cost of a continuously adjusted replicating portfolio.

Evidence

The preceding sections have shown that economics was crucial in legitimating the establishment of an options exchange, but that the processes of establishment, and behavior after the CBOE was set up, involved action at odds with homo œconomicus’s rational egoism. We now turn to the impact of the option pricing theory of Black and Scholes (1973) and Merton (1973) on the CBOE. Earlier academic work on options (e.g., Malkiel and Quandt 1968, 1969) had involved either empirical, econometric analyses or elaborate theoretical models that contained parameters whose values could not be measured in any straightforward way. 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 Black-Scholes arbitrage-based derivation: the option’s fair price is the cost of the replicating portfolio, enforced by arbitrage convergence.
• XREF: connects to: Pricing under a risk-neutrality fiction yields the same option price as arbitrage pricing. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1283; Options can be synthetically manufactured by shifting between stocks and cash as prices move. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 793; Option prices equal the cost of a portfolio that replicates the option’s payoff — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95

Related

• Option prices equal the cost of a portfolio that replicates the option’s payoff (similarity 0.95)
• Pricing under a risk-neutrality fiction yields the same option price as arbitrage pricing. (similarity 0.88)
• Option prices are set entirely by arbitrage, independent of risk attitudes or probabilities (similarity 0.87)
• Black-Scholes legitimized options despite fitting prices only approximately (similarity 0.86)
• Options can be synthetically manufactured by shifting between stocks and cash as prices move. (similarity 0.86)
• Modern options pricing derives from arbitrage logic, not directional beliefs. (similarity 0.85)
• Black-Scholes-Merton pricing fit observed options data only approximately at launch. (similarity 0.85)
• The arbitrage argument produces the Black-Scholes partial differential equation. (similarity 0.84)
• The option price is independent of the stock’s expected return. (similarity 0.84)
• The Black-Scholes theory reframed options trading as legitimate efficient pricing rather than gambling. (similarity 0.83)
• Option pricing theory did not describe markets but remade them in its own image (similarity 0.83)
• Market prices converged toward Black-Scholes values within a few years of the CBOE’s founding (similarity 0.83)
• Option market prices initially diverged from the Black-Scholes model but converged (similarity 0.83)
• Pre-Black-Scholes option models relied on unmeasurable parameters (similarity 0.83)
• the risk-neutral valuation insight lets options be priced by discounting at the riskless rate (similarity 0.83)

Broader Connections

• Options can be synthetically manufactured by shifting between stocks and cash as prices move. #corroborates (0.95) — Donald MacKenzie, An Engine, Not a Camera, 793
• Pricing under a risk-neutrality fiction yields the same option price as arbitrage pricing. #expands (0.85) — Donald MacKenzie, An Engine, Not a Camera, 1283