Final answer:
The minimum price of the call option can be calculated using put-call parity, taking into account the spot and forward rates of the Swiss franc, the striking price, and the annualized six-month Eurodollar rate.
Step-by-step explanation:
The minimum price of a six-month American call option with a striking price of $0.6836, given the spot Swiss franc is $0.7072 and the six-month forward rate is $0.6986, in a rational market, can be computed using the concept of put-call parity. Considering an annualized six-month Eurodollar rate of 3.5%, the minimum value can be determined by adjusting the option with current market conditions and interest rates. The formula includes utilizing the present value of the strike price discounted at the Eurodollar rate.
To calculate the minimum price of the call option, you adjust the striking price by the present value factor for the Eurodollar rate over the six months period. This represents the least amount the call option could be worth in a rational market where no arbitrage opportunities exist. It's not just the intrinsic value (current spot price - striking price) that is considered, but also the time value of money, adjusted for the prevailing interest rate over the period until the option's expiration.