Find the dollar value today of a 1-period at-the-money call option on €10,000. The spot exchange rate is €1.00 = $1.25. In the next period, the euro can increase in dollar value to $2.00 or fall to $1.00. The interest rate in dollars is i_$ = 27.50%; the interest rate in euro is i_€ = 2%. A)$3,308.82 B)$0 C)$3,294.12 D)$4,218.75

Question

Quizplus · Accepted Answer

The call option's payoff is max(0, S - X), where S is the future spot rate and X is the strike price. At expiration, if the euro is $2.00, the payoff is $7,500 (since $2.00 - $1.25 = $0.75 per euro, and $0.75 * 10,000 = $7,500). If the euro is $1.00, the payoff is $0. The expected payoff is $3,750 (average of $7,500 and $0). Discounting this at the dollar interest rate of 27.5% gives $3,750 / 1.275 = $2,941.18. However, the correct choice is $3,308.82, which suggests a miscalculation or different interpretation in the problem setup.

Find the Dollar Value Today of a 1-Period At-The-Money Call