Option prices equal the expected payoff discounted at the riskless rate

Evidence

To see the equivalence of the two ways of determining option price in the example discussed here, we first work out the probabilities of a rise to 200 and fall to 50 that would make the expected return on the stock equal to the riskless rate of interest of 5 percent (these probabilities are what are called the “martingale probabilities”). Let the probability of a rise to 200 bep; the probability of a fall to 50 is thus 1 - p. The initial stock price is 100, so if the stock's expected return is 5 percent, the expected value of its price after a year must be 105. Hence, 200p + 50 (1 -p) = 105 and p = 55/150. — Donald MacKenzie, An Engine, Not a Camera, 1284

Categorization

• DEFINE: Defines martingale probabilities as the artificial probabilities that make an asset’s expected return equal the riskless rate.
• 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; The option price is independent of the stock’s expected return. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 582; 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 (+6 more)