# option prices

schweser practice test exam 2 afternoon session number 116. They say an american style call option must be worth at least as much as an otherwise identical euro style option and has the same minimum. Same minimum? The extra option to exercise should make the american minimum more than the minimum of the euro.

Long options have limited downside, ie 0. Amer and Euro options can both expire wothless. The downside is limited to the premium paid for both. Its is true though that an Amer option will be worth more than a Euro option up until expiration.

wait, so you are saying the amer option minimum should be more than the euro option minimum?

For both, if tou own the option, the minimum value is 0. The am option is usually worth more before expiration though, all else equal The am option can be exercised at any time up to expiration, which gives it more value relative to the eur option, which can only be excersised on one date. Ex: stock at 50, both amer and euro call option to buy at 40, 2mos until expiration. The amer option wil cost more, because it can be excersised now for a profit, but the euro cannot. There is risk that the stock may fall below 40 by expiration, and both options become worthless. The amer option has the ‘option’ to lock in a gain, the euro doesn’t. Regardless, both have a minimum value of 0. Ie if you have a call option to buy Walmaert for 300/share that expires in a month, both an amer and euro will be worth 0. Same idea as a putable bond. A bond putable at any time will be worth more than the same bond that is only putable on a specific date.

it might be easier if i just post the question. what are the minimum value of an american style and a european style 3 month call option with a strike price of \$80 on a non-dividend paying stock trading at \$86 if the risk free rate is 3%? ----american ----- european a. \$6.00 ----- \$6.00 b. \$6.59 ----- \$6.00 c. 6.59 ---- 6.59 answer is c. explanation: an american style call option must be worth at least as much as an otherwise identical euro call option and has the same minimum value. this fact alone eliminates choice b. since the american style call is in the money and therefore must be worth more than the \$6 difference between the strike price and the exercise price, you can eliminate response a and select c without calculating the exact minimum value, which is given by max [0, S - X / (1 + RFR) ^ (T-t)] = max [0, 86 - 80 / (1.03) ^ 0.25] = \$6.59 ---------------------------- I see the calculation and I see in the book that both style options have the same minimum… but I want to grasp this conceptually and intuitively as to why choice b has to be eliminated. This question is assuming no transaction costs. If the market prices in choice c was presented in the market, nobody would buy the euro option either driving the american option price higher or driving the euro option price lower. Either way, the american option minimum has to be higher than the euro minimum. Does this make sense?

Just watch the relevant part of the elan video on options. Its on their samples page for free. They really do an excellent job I think.

Question helps. They are saying the minimum value at this specific time. Which would then be ITMoney amount times RFR. This “minimum value” is assuming 0 volatility, similar to pricing a futures contract. In reality, the American option would be priced higher than the Euro. This is the theory portion they are teaching. Both would have a minimum value at this time of the ITMoney amount and RFR Again, add volatility, and the actual prices change. The minimum they refer to is the arbitrage free prices. This help?

Min value of an amer call and euro call with the EXACT same characteristics aside from option to exercise early on the amer call is the same. Max value of amer call and euro call are also calculated the same but it is understood that the amer call is AT LEAST equal to the euro call (the premium may be greater than the euro call)… At this point, I wouldn’t be looking into understanding why that is, but it is that way…