### CFA Practice Question

There are 206 practice questions for this study session.

### CFA Practice Question

Consider call and put options expiring in 42 days, in which the underlying is at 72 and the risk-free rate is 4.5%. The underlying makes no cash payments during the life of the options. Find the lower bounds for European and American calls and puts with exercise prices of 70 and 75.

European options
• 70 call: Max [0, 72 - 70/(1.045)0.1151] = Max[0, 2.35] = 2.35
• 75 call: Max [0, 72 - 75/(1.045)0.1151] = Max[0, -2.62] = 0
• 70 put: Max [0, 70/(1.045)0.1151 - 72] = Max[0, -2.35] = 0
• 75 put: Max [0, 75/(1.045)0.1151 - 72] = Max[0, 2.62] = 2.62
B. American options
• 70 call: Max [0, 72 - 70/(1.045)0.1151] = Max[0, 2.35] = 2.35
• 75 call: Max [0, 72 - 75/(1.045)0.1151] = Max[0, -2.62] = 0
• 70 put: Max(0, 70 - 72) = 0
• 75 put: Max (0, 75 - 72) = 3

User Comment
cuong Is there anybody please tell me how we can get 0.1151???
Pooh 42 days out of 365 per year = 42/365=.1151
Nancyz I think the answers for american options calls are wrong. The low bound for American option price is its current intrinsic value: max (0, 72-70)=2, for 75 call =0.
Nancyz never mind. the answer is correct. the lower bound of the european call holds for american calls.
stefdunk does anyone know why we use the time value of money for american calls, but not for puts?
johnsk Because you can realize the profit right away by exercising the American put option.
EK65 We use time value for american call because otherwise an american option price will be lower than european, which is not possible. Therefore the lower boundary for euro option holds for american. The situatio is different for put, thus we don't need to use the same formula
0is4eva 42 days ==> interst rate factor = int = 1/[(1+0.045)^(42/365)]
S = 72
Solve for X = 70, 75 for put/call Eur/Am style.

Eur 70 call = S - X int = 72 - 70 * int = 2.35
Eur 75 call = S - X int = 72 - 75 * int = neg. --> 0
Eur 70 put = X int - S = 70 * int - 72 = neg. --> 0
Eur 75 put = X int - S = 75 * int - 72 = 2.62

Lower bound for Am options is its intrinsic value or value of Eur option.
Am 70 call: S - X = 72 - 70 = 2 but 2.35 for Eur option is greater --> 2.35
Am 75 call: S - X = ... = 0
Am 70 put: X - S = 70 - 72 = neg. --> 0
Am 75 put: X - S = 75 - 72 = 3

Never optimal to exercise Am call on non-dividend-paying stock before expiration date. Strike price paid later (interest earned), no dividend is lost on stock, plus some chance that price of stock will fall below X. (If an overpriced stock it is different).
Rotigga This is an excellent question. It really hammers home the fact that, ceterus paribus, an American option cannot be cheaper than a European option.
gazza77 isnt the convention for interest rate calculations to use 360 days in a year?
gill15 Great Question. Boom got it. It`s the unit summarized.