A Japanese company purchased currency options to hedge AUD 1 million payable. The exercise price of the option is JPY100/AUD with a premium of JPY5/AUD. The spot rate became JPY110/AUD at the time of maturity. Which of the following statements is true?

Question

BlackTom AI · Accepted Answer

We start by restating the situation and options to ensure clarity: a Japanese company has hedged a currency payable of AUD 1 million by buying currency options with an exercise price (strike) of JPY 100 per AUD and a premium of JPY 5 per AUD. At maturity, the spot rate is JPY 110 per AUD. The question asks which statement is true about the outcome.

Option a: "The company will not exercise the option ending up with JPY 100 million."
- This would imply exercising is not done and ending up with 100 million JPY, which ignores the effect of the premium and the correct calculation of the exercise payoff. If the option is not exercised, the company would still have paid the 5 JPY premium per AUD, a sunk cost, and would acquire AUD at the spot rate if needed. The stated figure of 100 million JPY is inconsistent with the mechanics of exercising or not exercising given the strike and the premium.

Option b: "The company will end up with JPY 105 million by exercising the option."
- This matches the standard payoff for a call option on currency when the spot rate exceeds the strike: you exercise to buy AUD at the strike price (100 JPY per AUD), paying 100 million JPY for 1 million AUD, and you also have paid a premium of 5 million JPY (1,000,000 AUD × 5 JPY/AUD). The total cash outflow is 100m + 5m = 105m JPY. Since the spot at maturity is 110 JPY/AUD, exercising at 100 JPY is favorable relative to paying 110 JPY/AUD in the market, so the 105 million figure correctly reflects the combined exercise payment and the premium.

Option c: "The company will end up with JPY 100 million by exercising the option."
- This ignores the premium. Exercising requires paying 100 JPY per AUD for 1,000,000 AUD, i.e., 100 million JPY, but you must also account for the premium of 5 million JPY paid upfront. The total would be 105 million JPY, not 100 million, so this statement is incomplete.

Option d: "The company will not exercise the option ending up with JPY 110 million."
- If the option is not exercised, the company would settle based on the spot rate at 110 JPY/AUD for 1,000,000 AUD, i.e., 110 million JPY, but you must still include the premium paid as a sunk cost. The statement ignores the premium and also assumes no exercise action, which makes the 110 million figure incomplete as a representation of total cost after considering the premium.

In summary, evaluating the mechanics of a currency call option hedge shows that exercising the option when the spot exceeds the strike yields a total outlay of 105 million JPY (100 million for the purchase of AUD at the strike plus 5 million premium). The other options either omit the premium, misstate the total cost, or mischaracterize whether exercising would occur, given the favorable spot versus strike comparison.

A Japanese company purchased currency options to hedge AUD 1 million payable. The exercise price of the option is JPY100/AUD with a premium of JPY5/AUD. The spot rate became JPY110/AUD at the time of maturity. Which of the following statements is true?

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