Jamal Awil

← An Engine, Not a Camera

The option's present value to a riskneutral investor is thus $18. [fact]

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, loc. 1285