the risk-neutral valuation insight lets options be priced by discounting at the riskless rate
Evidence
“Rather suddenly, it came to us,” Black later recalled. “If the stock had an expected return equal to the [riskless] interest rate, so would the option. After all, if all the stock’s risk could be diversified away, so could all the option’s risk. If the beta of the stock were zero, the beta of the option would have to be zero too… The discount rate that would take us from the option’s expected future value to its present value would always be the [riskless] interest rate.” — Donald MacKenzie, An Engine, Not a Camera, 583
Categorization
- DEFINE: Captures the core risk-neutral valuation insight in Black’s own words, a foundational definitional move for the whole modern derivatives-pricing framework.
- ADDENDUM: This pricing logic connects to the performativity thesis: the model that assumed riskless-rate discounting then helped make markets behave that way via replication and hedging.
- XREF: connects to: Discounted cash flow valuation treats the future ambivalently, valuing yet discounting it. — Ève Chiapello, Financialisation of Valuation, 30; Thorp approximated warrant values by assuming stocks rise at the riskless interest rate. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 557; The option price is independent of the stock’s expected return. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 582 (+6 more)
Broader Connections
- Option prices equal the expected payoff discounted at the riskless rate
#expands(0.98) — Donald MacKenzie, An Engine, Not a Camera, 1284 - Pricing under a risk-neutrality fiction yields the same option price as arbitrage pricing.
#corroborates(0.90) — Donald MacKenzie, An Engine, Not a Camera, 1283 - Risk-neutral valuation yields the identical option price as arbitrage arguments
#expands(0.85) — Donald MacKenzie, An Engine, Not a Camera, 1285 - Pre-Black-Scholes option valuation needed investor risk attitude as an unobservable input
#qualifies(0.80) — Donald MacKenzie, An Engine, Not a Camera, 536