As a hypothetical example, an importer has to pay USD 200,000 for imports on the expiry date. It holds a zero-cost option that combines buying a USD call option and selling a USD put option, both with a strike of 145 yen per dollar and an amount of USD 200,000. If the spot exchange rate at expiry is 135 yen, which statement about this combination is correct?
Quiz: FX Exotics
Last reviewed: September 25, 2026
This is a draft, shown for review before publication.
5 questions to check your understanding of the chapter “FX Exotics”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.
Question 1
Answer and explanation
Answer: A
At expiry the spot exchange rate is 135 yen, below the strike of 145 yen (a stronger yen), so the sold put is exercised and the importer has to buy dollars at 145 yen. Compared with buying at the spot rate, the difference is (135 − 145) × USD 200,000 = −2 million yen. The loss widens as the yen strengthens and does not stop as long as the rate keeps falling.
If you assume that the gain on the call bought offsets the loss on the sold put, you are likely to pick the choice that says no profit or loss arises. At a spot rate of 135 yen, exercising a call at 145 yen would not pay off, so the call is not exercised and nothing offsets the loss on the put.
If you assume that the loss on a sold put is limited to the premium received, you are likely to pick the choice that says the loss is limited. A zero-cost option offsets the premium received on the option sold against the premium paid on the option bought, so that no premium changes hands. Even with no premium changing hands, a loss arises once the sold put is exercised, and the loss is not limited to the amount of premium received.
If the spot exchange rate at expiry is 155 yen, the importer exercises the call and buys dollars at 145 yen, which is (155 − 145) × USD 200,000 = 2 million yen better than buying at the spot rate. If the importer holds this combination for the same amount as its payment and treats it as a hedge of the payment, its price for the dollars is fixed at 145 yen whether the yen weakens or strengthens. At 135 yen, it gives up the saving it would have made by buying at the spot rate. If it has sold a put for more than its payment, the loss on the excess over the payment grows as the yen strengthens.
Learn more: Overview of Exotic FX Products
Question 2
A power reverse dual (PRD) note is a bond for investors that repays its principal in yen. Which statement about the interest and early redemption of a PRD note is correct?
Answer and explanation
Answer: D
The interest on a PRD note changes with the exchange rate on each interest payment date: it is higher when the yen is weaker and lower when it is stronger. The interest cannot fall below 0%. The issuer has the right to redeem the note early on each interest payment date, and the investor receives the price of selling this right as extra yield.
If you assume that because the investor receives extra yield, the investor must hold a favorable right, you are likely to pick a choice in which the investor has the right to redeem. The extra yield is not the price of holding a right but the price of selling a right to the issuer. The choices in which interest is higher when the yen is stronger reverse the direction in which interest moves with the exchange rate.
Learn more: Overview of Exotic FX Products
Question 3
As a hypothetical example, an importer, Company K, has bought a USD call (JPY put) on USD 1 million. The strike price is 148 yen, the lower barrier is 140 yen, and the upper barrier is 160 yen. It is a double knockout, and the current spot rate is 150 yen per dollar. If the rate moves between 141 yen and 158 yen during the period and the spot rate at expiry is 152 yen, how much is the payoff at expiry, excluding the premium?
Answer and explanation
Answer: A
The rate touched neither the upper nor the lower barrier during the period, so the right is still alive. The spot rate at expiry of 152 yen is above the strike price of 148 yen, so the payoff is (152 − 148) × USD 1 million = 4 million yen.
0 yen is the value you get if you assume the barrier was touched and the right disappeared. If the rate had touched 160 yen or 140 yen even once during the period, the right would have disappeared, and the payoff would be 0 yen even with a rate of 165 yen at expiry. In this example, neither barrier was touched.
12 million yen counts the difference from the upper barrier of 160 yen, (160 − 148) × USD 1 million, instead of the strike price. 2 million yen counts the difference from the current spot rate of 150 yen, (152 − 150) × USD 1 million. The payoff of a call is set by the difference between the spot rate at expiry and the strike price.
Learn more: FX Barrier Options
Question 4
When the gamma of a TARF (target redemption forward) is computed by combining Monte Carlo with finite differences, which statement about the size of the shift in the rate (the bump) is correct?
Answer and explanation
Answer: B
A smaller bump reduces the bias of the finite-difference approximation, but the Monte Carlo estimate varies more. The problem is large for gamma, a second-order sensitivity, and many paths are needed to obtain a reliable value.
The choice that both the bias and the variation become smaller overlooks that the variation grows. The choice that the bias grows has the direction reversed. The choice that the variation is unaffected does not fit the fact that a smaller bump increases the variation.
Learn more: Target Redemption Forward (TARF)
Question 5
As a hypothetical example, the coupon rate of a PRDC is set by multiplying the dollar coupon rate by the ratio of the exchange rate on the interest payment date (yen per dollar) to the reference rate, and then subtracting the yen coupon rate. The dollar coupon rate is 8%, the yen coupon rate is 6%, the reference rate is 140 yen, the floor is 0, and there is no cap. What is the highest exchange rate on the interest payment date at which the coupon rate is zero?
Answer and explanation
Answer: C
The level at which the coupon rate becomes zero is the reference rate × the yen coupon rate ÷ the dollar coupon rate = 140 × 6% ÷ 8% = 105 yen. If the exchange rate is 105 yen or below, the value of the formula is 0 or below, and the floor of 0 becomes the coupon rate. At exactly 105 yen, 8% × 105 ÷ 140 − 6% = 0.
140 yen treats the reference rate as the level at which the coupon rate is zero. At the reference rate, the coupon rate is 8% − 6% = 2%, which is positive. About 187 yen is 140 × 8% ÷ 6%, which swaps the dollar and yen coupon rates. At an exchange rate of 187 yen, the coupon rate is 8% × 187 ÷ 140 − 6%, about 4.7%, not zero. 35 yen is 140 × (8% − 6%) ÷ 8%, which uses the difference between the dollar and yen coupon rates. At 35 yen, the formula gives 8% × 35 ÷ 140 − 6% = −4%, so the floor makes the coupon rate zero, but it is not the highest exchange rate at which the coupon rate is zero.
Learn more: Power Reverse Dual Currency (PRDC)