Risk-neutral valuation yields the identical option price as arbitrage arguments

Evidence

If the stock’s price rises to 200, the call option is worth 50; if the price falls to 50, the option is worthless. So the expected value of the option's payoff is 50 x p = 50 x (55/150) = 18.33. The option’s present value to a riskneutral investor is thus 18.33 discounted at the riskless interest rate of 5 percent: 18.33/1.05 = $17.46, which is equal to the price as determined by arbitrage. — Donald MacKenzie, An Engine, Not a Camera, 1285

Categorization

• DEFINE: Concrete demonstration of risk-neutral valuation, where the option price is the discounted expected payoff under martingale probabilities.
• XREF: connects to: Market arbitrage requires only that investors prefer more wealth to less, not risk preferences — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 180; Risk attitude determines how an investment’s value differs from its expected payoff — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 534; Pre-Black-Scholes option valuation needed investor risk attitude as an unobservable input — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 536 (+8 more)

Broader Connections

• Option prices equal the expected payoff discounted at the riskless rate #corroborates (1.00) — Donald MacKenzie, An Engine, Not a Camera, 1284