Pricing under a risk-neutrality fiction yields the same option price as arbitrage pricing.
Evidence
Thus far, the argument used to determine the option price is simply the binomial analogue of Black-Scholes-Merton option pricing. Risk-neutral valuation as put forward by Cox and Ross involves assuming (a) that all investors are risk neutral, and so the value to them of risky investments is the present value of the expected payoff of these investments; and (b) that “the expected returns on both stock and option must equal the riskless rate” of interest (Cox and Ross 1976, p. 153). Cox and Ross’s claim was that the price of an option as worked out under these assumptions must be its arbitrage-determined price in our original world (in which we assumed nothing about expected returns or attitudes to risk). — Donald MacKenzie, An Engine, Not a Camera, 1283
Categorization
- DEFINE: Explains risk-neutral valuation: a fictitious assumption that nevertheless replicates the arbitrage-determined price.
- XREF: Core to this reader’s performativity goal: the risk-neutral fiction does real pricing work in markets. — connects to: Option price must equal the cost of a continuously adjusted replicating portfolio. — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95; the risk-neutral valuation insight lets options be priced by discounting at the riskless rate — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 583; Option prices are set entirely by arbitrage, independent of risk attitudes or probabilities — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 608 (+7 more)
Broader Connections
- Risk-neutral valuation yields the identical option price as arbitrage arguments
#corroborates(0.98) — Donald MacKenzie, An Engine, Not a Camera, 1285 - Option prices equal the expected payoff discounted at the riskless rate
#expands(0.85) — Donald MacKenzie, An Engine, Not a Camera, 1284 - The arbitrage argument produces the Black-Scholes partial differential equation.
#expands(0.80) — Donald MacKenzie & Yuval Millo, Constructing a Market, Performing Theory, 95 - Modern options pricing derives from arbitrage logic, not directional beliefs.
#qualifies(0.75) — Donald MacKenzie, An Engine, Not a Camera, 1454