# Prior to expiration the maximum value of CALL + PUT options is...

Prior to expiration the maximum value of CALL + PUT options is… I understand options, but the language here throws me off… someone else have a problem with that. The maximum value of a call option is the underlying price; it makes no sense to pay more for the right to buy the underlying than the value of the underlying itself, and the maximum value of an American put is the exercise price because the best outcome would be if the stock fell to zero, the holder could capture the value of the exercise price. Someone have a way of looking at this and saying it in English…

Prior to expiration – means the option has not yet expired. Assuming American: So for a Call Max (0, S-X) --> not yet expired. So Max value will be when X=0 --> S underlying price. Put: Max(0, X-S) --> not yet expired --> Max value is when S = 0 --> X (Exercise price). CP

Is there a different way of looking at it without those notations? I don’t process that for some reason, but see it very clearly with numbers…

PRIOR to expiration just means you have to take the risk-free into account (AT EXPIRATION means american/european options are the same, dont need to take into account risk-free) so, calls are the same: Max value is S (the stock price) for puts: max value for american is X max value for european is X/(1+r)^t

Not sure if this is what you’re asking, but the maximum value of a call before expiration is theoretically infinite, whereas a put is maxed out at the strike price you minus the premium you paid. Stocks have no upper limit, but a lower limit of 0, ie. bankrupt. Is that what you were asking?

you simultaneously buy a call and sell a put with identical exercise price X. The effect of that portfolio is the same as a long option position Long call + short put = Synthetic Long: If you also have a security to sell then the outcome wouldn’t depend on a price of security - box trade. Profit = S−X + P−C But eventually that profit would be zero (after all arbitrageurs attempt to profit) . Plus considering time value of future cash flows --> S+P = C+ X/(1+r)^T and then you may derive put/call

I’m not sure I agree with Malnoll regarding the absence of an upper limit on call prices prior to expiration. I think there is a limit to the maximum value of a call option before expiration, and that limit is the stock price. No one will pay more for a right to buy something than the cost of the underlying asset. For example, why would you pay \$10000 for the right to buy a car worth only \$1000. Makes more sense simply to buy the car. Even if the car turns out to be a collector’s item that could fetch \$1 million, you would be better off having bought it outright at \$1000 than having bought the call option at \$10000. Thus, the upper limit for call options (whether European or American) is the stock price.

cheb, i think malnoll thought of the situation you describe, but the stock price can rise to infinity (in theory at least).

I see what you’re saying, that in an unlikely, never going to happen case, if a stock jumped up X0000%, it would be so deep in the money that nearly all of the value would be the underlying stock price.

if you’ve got the schweser notes, do you remember how they had TWO tables with the option max/min bounds? the first one was more general, and the second one was more restrictive (and included the use of the risk-free)… i’m pretty sure this refers to the difference between “prior to maturity” and “at maturity”

One way to remember the tables is that the table for values prior to expiration reduces mathematically to the table for values at expiration when T-t = 0. So you only really need to remember the table for upper and lower bounds prior to expiration. That table is basically intuitive, except that you discount the strike price at the risk free rate wherever it crops up, with the one exception of the American put.