Assume that the dollar-euro spot rate is $1.28 and the six-month forward rate is $F_{T}=S_{t} e^{\left(r_{\$}-r_{€}\right)^{T}}$ = $1.28 $e ^{.01 \times .5}$ = $1.2864.The six-month U.S.dollar rate is 5 percent and the Eurodollar rate is 4 percent.The minimum price that a six-month American call option with a striking price of $1.25 should sell for in a rational market is

Question

Quizplus · Accepted Answer

To calculate the minimum price of a six-month American call option with a striking price of $1.25, we need to use the following formula:

Call Option Price = Max[(Current Spot Price - Striking Price), 0] - Cost of Carry

Here, the Cost of Carry = (Foreign Interest Rate - Domestic Interest Rate) x Time to Expiration

= (4% - 5%) x 0.5

= -0.5%

Now, let's calculate the values for the formula:

Current Spot Price = $1.28 
Striking Price = $1.25 
Max[(Current Spot Price - Striking Price), 0] = $0.03 (because the spot price is higher than the striking price)

Therefore, the minimum price of the call option is:

Call Option Price = $0.03 - (-0.5% x $1.28 x 0.5)

= $0.03 - $0.0032

= $0.0268 or 2.68 cents

However, since the options cannot be sold for fractions of a cent, we must round up to the nearest cent, which gives us the final answer of 3.55 cents (choice C).

Assume That the Dollar-Euro Spot Rate Is $1 FT=Ste(r$−r€)TF_{T}=S_{t} e^{\left(r_{\$}-r_{€}\right)^{T}}FT​=St​e(r$​−r€​)T = $128

Assume That the Dollar-Euro Spot Rate Is $1 $F_{T}=S_{t} e^{\left(r_{\$}-r_{€}\right)^{T}}$ = $128