An American company has a 60 day payable of €1 million. A bank writes the American company a call option for a quantity of €1 million and with maturity in 60 days. The maturity date of the option is the same as the date of the payable. The call option has a strike price of $1.10. The option premium is $0.01; therefore the total premium paid is $10,000.

If the spot rate for the euro is $1.08 in 60 days, which of the following is a correct statement?

Question

An American company has a 60 day payable of €1 million. A bank writes the American company a call option for a quantity of €1 million and with maturity in 60 days. The maturity date of the option is the same as the date of the payable. The call option has a strike price of $1.10. The option premium is $0.01; therefore the total premium paid is $10,000.

If the spot rate for the euro is $1.08 in 60 days, which of the following is a correct statement?

BlackTom AI · Accepted Answer

The scenario involves an American company with a euro-denominated payable of €1,000,000 due in 60 days. The bank provides a call option on euros for €1,000,000 with a strike price of $1.10 per euro and a premium of $0.01 per euro, totaling $10,000.

Option 1: "Including the option premium paid, the cost of the payable in dollars is $1,090,000." If the spot rate at maturity is $1.08/€, exercising the call option is not advantageous because buying euros at $1.10/€ would be more expensive than the market rate. Instead, the company would buy €1,000,000 at the prevailing spot rate of $1.08/€, costing $1,080,000. Adding the $10,000 premium yields a total of $1,090,000. This aligns with a hedge that limits downside (and the premium is the cost of the hedge) while reflecting the actual cash outlay if the option is not exercised.

Option 2: "Including the option premium paid, the cost of the payable in dollars is $1,110,000." This would imply exercising the option at $1.10/€ despite the actual market rate being $1.08/€ in 60 days. Since the market rate is cheaper than the strike, exercising would be irrational and would incur unnecessary extra cost, making $1,110,000 incorrect under the given spot.

Option 3: "The American company is a speculator and has a loss of $10,000." To characterize the company as a speculator is not warranted by the hedging arrangement described. The premium paid ($10,000) is the cost of obtaining protection. Whether that results in a net loss depends on the actual cash outlay compared with the unhedged scenario; with a 60-day spot of $1.08/€, the total outlay with hedging is $1,090,000, which includes the hedging premium. Calling this a pure speculative loss ignores the hedging purpose and the alternative of paying the spot rate.

Option 4: "The American company is a speculator and has a loss of $30,000." This statement incorrectly aggregates costs: the premium is $10,000, and the alternative unhedged outlay at the spot rate would be $1,080,000 if no option existed. The $30,000 figure does not emerge from the provided numbers or the described hedging strategy, and labeling the firm a speculator while asserting a $30,000 loss is not supported by the math here.

In summary, the key financially correct point is that, with a spot of $1.08/€ at maturity, the hedged path costs $1,080,000 for the euros plus the $10,000 premium, totaling $1,090,000, since exercising the option at $1.10/€ would be more expensive than buying euros at the market rate. The other options misstate the cost when the spot is $1.08/€ or make incorrect characterizations about the nature of the hedge and the size of the loss.

类似问题

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