Assume the spot Swiss franc is $0.7000 and the six-month forward rate is $0.6950. What is the minimum price that a six-month American call option with a strik-ing price of $0.6800 should sell for in a rational market

The minimum price for the American option is 2 cents.

We can arrive at this answer in the following format:

%

With that, we can say that the minimum price is equal to 2 cents.

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2 cents

Explanation:

The spot price = $0.7000 = 70 cents, The forward rate = $0.6950 = 69.5 cents and the call option with striking price = $0.6800 = 68.00 cents

The annualized six month rate = 3 1/2 % = 3.5 %, therefore the rate = r/n, where n is the number of period per year = 2. Therefore r/n = 3.5% / 2 = 0.035 / 2 = 0.0175

The minimum price = Maximum (spot price - striking price, (forward rate - striking price) / (1 + 0.0175), 0) = Maximum(70 - 68, (69.5 - 68)/ 0.0175, 0)

Minimum price = Maximum (2 , 1.47, 0) = 2 cents

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