Schweser page 164: “The max val of either an American or European call option at any time t is the time-t share price of the underlying stock. This makes sense because no one would pay a price for the right to buy an asset that exceeded the asset’s value.” Wait a second. What “maximum value” are we talking about here? Exercise price? Intrinsic value? (i.e. greater of (s-x) or zero)? Option value (i.e. intrinsic value + time value)? I think they mean intrinsic value, because then it would make sense that the max val would be s, i.e. when x = 0. Could someone please clarify?
cnd, interesting question. They must mean the total option value (i.e. intrinsic + time). As Schweser mentioned, no one would pay more for the right to buy an asset than the value of the asset, which as you said, for common stock underlying a call option, is maximized when the exercise price equals zero. The time value must drop to zero for an option like this, does that sound about right?