The option price is independent of the stock’s expected return.

Evidence

Like Black, Scholes was “amazed that the expected rate of return on the underlying stock did not appear” in the equation (Scholes 1998, p. 481). This prompted Black and Scholes to experiment, as Thorp had done, with setting the expected return on the stock as the riskless rate of interest. They substituted this rate for the expected rate of appreciation of the stock price in Sprenkle’s formula for the expected value of the payoff of a warrant at expiration (equation 1 in appendix Q. To get the option or warrant price, they then had to discount that expected payoff, in other words to work out its present value. — Donald MacKenzie, An Engine, Not a Camera, 582

Categorization

• QUESTION: Worth chasing: how did Black and Scholes justify discarding the stock’s expected return, and why was this so counterintuitive to them?
• DEEPTHINKING: That the volatility-driven price ignores the drift/expected return is one of the deepest, most counterintuitive results in financial economics.
• XREF: connects to: Thorp approximated warrant values by assuming stocks rise at the riskless interest rate. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 557; Option prices equal the expected payoff discounted at the riskless rate — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 1284; 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 (+3 more)

Broader Connections

• the risk-neutral valuation insight lets options be priced by discounting at the riskless rate #corroborates (0.92) — Donald MacKenzie, An Engine, Not a Camera, 583
• Option prices equal the expected payoff discounted at the riskless rate #corroborates (0.90) — Donald MacKenzie, An Engine, Not a Camera, 1284
• Option prices are set entirely by arbitrage, independent of risk attitudes or probabilities #expands (0.85) — Donald MacKenzie, An Engine, Not a Camera, 608
• Risk-neutral valuation yields the identical option price as arbitrage arguments #corroborates (0.85) — Donald MacKenzie, An Engine, Not a Camera, 1285
• Leverage amplifies percentage returns, making options riskier than underlying stock #qualifies (0.72) — Donald MacKenzie, An Engine, Not a Camera, 535