FX Options

Companies with foreign currency payments or receipts fixed for the future, such as importers and exporters, can prepare for currency risk with a currency option as well as an FX forward, by buying a right. A bank that has sold a currency option to a company may hedge the currency risk of the option it sold in the spot foreign exchange market.

USD calls and JPY puts are the same right

In a currency option, the same right has two names depending on which of the two currencies you look at it from. The right to buy US dollars by paying yen is a call option to buy dollars and, at the same time, a put option to sell yen. This right is therefore called a "USD call / JPY put." The opposite right, to hand over dollars and receive yen, is a "USD put / JPY call"¹. For options on USD/JPY (the exchange rate stated in yen per dollar), the names put the dollar first.

The general mechanics of an option (calls and puts, buying and selling) are covered in Option Basics: Calls and Puts. What sets a currency option apart is that the underlying asset is a foreign currency and the purchase price is paid in another currency. When the buyer of a USD call exercises, it pays yen calculated at the strike price and receives dollars. An importer that will have to pay dollars later can buy a USD call to protect itself against a weaker yen. A company that will receive dollars later, such as an exporter, can buy a USD put to protect itself against a stronger yen.

How the premium is calculated and which currency pays it

The premium of a currency option is calculated as an amount of domestic currency per unit of foreign currency and multiplied by the principal to give the total². The principal is the amount of foreign currency bought or sold if the buyer exercises, which for a USD call is an amount in dollars. Premiums are stated in yen per dollar. Consider a hypothetical example in which a USD call with a principal of USD 1 million has a premium of 2.67 yen per dollar. The total is 2.67 yen × 1 million = 2.67 million yen.

The buyer pays this premium to the seller when the contract is made³. It may be paid in yen (the domestic currency) or in dollars (the foreign currency), and for some currency pairs paying in the foreign currency is the norm. The premium on a stock option is never paid in shares, so this is specific to currency options⁴.

Example: an importer buys a USD call

An importer that has bought a USD call can keep its cost of buying dollars at or below "strike + premium," however far the yen weakens⁵.

Consider a hypothetical example in which an importer, Company H, buys a USD call to prepare for paying USD 1 million for imports in six months. The spot exchange rate is 140 yen per dollar, the yen interest rate is 0.5%, and the dollar interest rate is 4.5%. Company H buys a USD call from a bank with a strike of 140 yen, an expiry of six months, and a principal of USD 1 million. It is a European option (an option that can be exercised only on the expiry date), and the premium is 2.67 yen per dollar (2.67 million yen in total). If the spot exchange rate at expiry is above 140 yen (a weaker yen), Company H exercises and buys dollars at 140 yen. At 140 yen or below, it abandons the right and buys dollars at that day's spot exchange rate.

Figure description

The profit or loss at expiry per dollar of a USD call with a strike of 140 yen, bought for a premium of 2.67 yen per dollar. The horizontal axis is the spot exchange rate at expiry, and the vertical axis is the profit or loss including the premium. At a spot exchange rate of 140 yen or below, the option is not exercised and the loss stays flat at −2.67 yen. Above 140 yen, each 1 yen move toward a weaker yen adds 1 yen to the profit or loss, which reaches 0 at 142.67 yen (the break-even point) and a profit of 7.33 yen at 150 yen. The loss is limited to the premium of 2.67 yen, and the profit keeps growing as the yen weakens.

Looked at on its own, the option loses the premium when the yen strengthens. What matters to Company H, though, is its total payment once the dollar purchase is included. The table below shows, for each spot exchange rate at expiry, how much yen Company H pays to buy USD 1 million in three cases: with no hedging, with an FX forward, and with a USD call. The contract rate of the FX forward is taken to be 137.23 yen, the forward exchange rate derived from the spot exchange rate of 140 yen, the yen interest rate of 0.5%, and the dollar interest rate of 4.5%⁶. The USD call column includes the premium of 2.67 million yen paid⁷.

If the yen weakens to 150 yen, Company H would pay 150 million yen without a hedge, but by exercising the USD call it pays 142.67 million yen. If the yen strengthens to 130 yen, Company H abandons the right and buys dollars for 130 million yen, or 132.67 million yen with the premium added. In that case it pays 4.56 million yen less than the 137.23 million yen under the FX forward. On the other hand, anywhere at or below 140 yen, where the option is not exercised, the USD call costs 2.67 million yen (the premium) more than having no hedge. Compared with the FX forward, the USD call costs less if the spot exchange rate at expiry is below 134.56 yen (137.23 − 2.67), that is, a stronger yen, and the FX forward costs less if it is above that level.

What determines the premium

The level of the premium depends on the spot exchange rate, the strike, the time to expiry, interest rates, and volatility (how much the exchange rate moves)⁸. A currency option involves two interest rates, one for yen and one for dollars. The theoretical premium is calculated by putting these five inputs into an option pricing formula. The formula is in the deep dive below.

The 2.67 yen in Company H's example is the value calculated with a spot exchange rate of 140 yen, a strike of 140 yen, an expiry of 0.5 years, a yen interest rate of 0.5%, a dollar interest rate of 4.5%, and volatility of 10%⁹. Changing one input at a time while holding the others fixed moves the premium as follows.

The premium is higher when volatility is larger and when the spot exchange rate is higher (a weaker yen). Cutting the dollar interest rate to 0.5%, the same as the yen rate, raises the premium to 3.94 yen. When the dollar interest rate is higher than the yen interest rate, the forward exchange rate is below the spot exchange rate (a stronger yen)¹⁰. In Company H's example, the forward exchange rate of 137.23 yen is below the strike of 140 yen, and to that extent the USD call, which pays off when the yen weakens, is cheaper.

Deep diveThe Garman-Kohlhagen formula

The premium of a currency option can be found with the Black-Scholes formula for stock options by using the yen (domestic currency) interest rate as the interest rate and putting the dollar (foreign currency) interest rate where the dividend yield goes¹¹. This works because the foreign currency plays the role of the stock, and the foreign interest rate plays the role of the dividend yield. The model that uses this formula is called the Garman-Kohlhagen model¹².

Let $S$ be the spot exchange rate (yen per dollar), $K$ the strike, $T$ the number of years to expiry, $r_d$ the yen interest rate, $r_f$ the dollar interest rate (both continuously compounded), and $\sigma$ the volatility. The premium $C$ of a USD call (yen per dollar) is then given by the following formula¹¹.

$$C = S e^{-r_f T} N(d_1) - K e^{-r_d T} N(d_2)$$ $$d_1 = \frac{\ln(S/K) + (r_d - r_f + \sigma^2/2)T}{\sigma\sqrt{T}}$$ $$d_2 = d_1 - \sigma\sqrt{T}$$

$N(\cdot)$ is the cumulative distribution function of the standard normal distribution. The formula is the Black-Scholes formula for a stock with a dividend yield, with the dividend yield $q$ replaced by $r_f$ and the interest rate $r$ replaced by $r_d$. In Company H's example ($S = K = 140$, $T = 0.5$, $r_d = 0.5\%$, $r_f = 4.5\%$, $\sigma = 10\%$), $d_1 = -0.247487$, $d_2 = -0.318198$, $N(d_1) = 0.402266$, and $N(d_2) = 0.375167$. With $e^{-r_f T} = 0.977751$ and $e^{-r_d T} = 0.997503$, the first term is 55.0642 yen and the second term is 52.3923 yen, and the difference, 2.6719 yen, is the premium.

How it differs from an FX forward

An FX forward is an obligation with no premium, whereas a long USD call is a right for which the buyer pays a premium when the contract is made¹³. A table comparing the two is in FX Forwards.

The seller's risk and trading in the market

The buyer of a currency option can lose at most the premium it paid. The seller is obliged to deliver if the buyer exercises and receives the premium in return for that obligation, but its loss has no theoretical limit¹⁴. In Company H's example, from the side of the bank that sold the option, a spot exchange rate of 150 yen at expiry means handing over dollars worth 150 yen each for 140 yen. Even after subtracting the premium of 2.67 yen it received, the bank loses 7.33 yen per dollar.

When importers, exporters, and investors trade currency options, the counterparty is a financial institution. Companies and investors use currency options to limit their currency risk, or to take on currency risk in pursuit of returns, and the financial institutions on the other side hedge in the spot foreign exchange market¹⁵.

According to Bank of Japan figures, foreign exchange turnover in Japan in April 2025 averaged 440.2 billion US dollars per business day, of which currency options accounted for 12.4 billion US dollars (2.8%)¹⁶.

Notes

1. Japan External Trade Organization (JETRO), "外国為替取引における先物予約と通貨オプションの違い" (The difference between forward exchange contracts and currency options, Trade and Investment Q&A, last updated July 2025, in Japanese), "Ⅰ. 通貨オプション取引" (I. Currency option transactions) in the answer. The source's "円プット・ドルコール・オプション" (yen put, dollar call option; our translation) can be written with the dollar first, as in "USD call / JPY put." ↩

2. Martin Haugh, "Foreign Exchange, ADR's and Quanto-Securities" (Columbia University, 2013), page 3, "Currency Options." The notional is the number of units of foreign currency that the buyer has the right to buy or sell, and the value of the option is N × C(X, t). ↩

3. JETRO, "外国為替取引における先物予約と通貨オプションの違い" (in Japanese), "Ⅰ. 通貨オプション取引" (I. Currency option transactions). The source says the buyer pays the premium "in advance, at the time of the contract" (our translation). ↩

4. Haugh, page 3, "Delta and the Option Premium." The source says the premium may be paid in the domestic currency or the foreign currency, that this does not happen with stock options, and that for some currency pairs it is natural to pay in the foreign currency. ↩

5. Central Council for Financial Services Information, "3-5 オプション取引活用の例（やさしいデリバティブ）" (Examples of using option trading, Easy Derivatives, in Japanese), "ヘッジング" (Hedging), "通貨オプションの例" (Example of a currency option). In the source's example, a person who plans to convert yen into dollars in three months buys a call to buy dollars at 120 yen, exercises it if the yen weakens, and abandons the right and buys dollars at the market rate if the yen strengthens. ↩

6. The contract rate of the FX forward, excluding the bank's margin, is the forward exchange rate obtained by applying half a year of the difference between the yen interest rate of 0.5% and the dollar interest rate of 4.5%, continuously compounded, to the spot exchange rate of 140 yen (140 × e to the power of −0.02 = 137.2278 yen), rounded to two decimal places. The formula is equation (1) on page 2 of Haugh. ↩

7. The table adds the 2.67 million yen premium paid when the contract is made directly to the payment at expiry. It ignores the interest on the premium over the six months from the contract to expiry. ↩

8. JETRO, "外国為替取引における先物予約と通貨オプションの違い" (in Japanese), "Ⅱ. 取引コスト・取引採算" (II. Transaction costs and profitability). The source says the level of the premium "is determined by factors such as the current market price, the strike price, the period to the expiry date, interest rates, and volatility (expected rate of fluctuation)" (our translation). ↩

9. Interest rates are treated as continuously compounded (the simulator does the same). Values are rounded to two decimal places. The intermediate values of the calculation are in the deep dive under "What determines the premium." ↩

10. Haugh, equation (1) on page 2. The forward exchange rate is the spot exchange rate multiplied by $e^{(r_d - r_f)T}$, so if $r_f$ is higher than $r_d$, it is smaller than the spot exchange rate (a stronger yen). ↩

11. Haugh, page 1 (the foreign currency plays the role of the "stock," and the foreign interest rate $r_f$ plays the role of the "dividend yield"), and equation (3) on page 3. The source's symbol $X_t$ corresponds to $S$ on this page and $\Phi$ to $N$, and this page writes $T - t$ as $T$. ↩ ↩²

12. OpenGamma, "Digital Forex Options" (2012), Section 2 "Pricing in Garman-Kohlhagen model." The paper describes the Garman-Kohlhagen model as the Black-Scholes model applied to the foreign exchange market, with one interest rate for each currency. ↩

13. JETRO, "外国為替取引における先物予約と通貨オプションの違い" (in Japanese), the opening of the answer and "Ⅰ. 通貨オプション取引" (I. Currency option transactions). ↩

14. JETRO, "外国為替取引における先物予約と通貨オプションの違い" (in Japanese), "Ⅰ. 通貨オプション取引" (I. Currency option transactions), covering the seller's obligation and that the loss is "theoretically infinite" (our translation), and "Ⅱ. 取引コスト・取引採算" (II. Transaction costs and profitability), covering that a buyer who abandons the right loses "at most the premium paid" (our translation). ↩

15. Bank of Japan Financial Markets Department, "通貨オプション取引の増加と市場取引への影響" (The increase in currency option trading and its effect on market transactions) (Bank of Japan Review, November 2007, in Japanese), pages 1–2, "通貨オプションが為替取引に与える影響" (The effect of currency options on foreign exchange trading), and Chart 2. ↩

16. Bank of Japan Financial Markets Department, "外国為替およびデリバティブに関する中央銀行サーベイ（2025年4月中 取引高調査）について：日本分集計結果" (Central Bank Survey of Foreign Exchange and Derivatives Market Activity, April 2025 turnover: results for Japan, in Japanese) (October 6, 2025), page 5, the "合計" (Total) row of Chart 1 "取引相手先別、取引種類別取引高（1 営業日平均）" (Turnover by counterparty and instrument, daily average) in Annex 1. The source's unit is 100 million US dollars, and the share is the source's figure. An English version is available: "Central Bank Survey of Foreign Exchange and Derivatives Market Activity in April 2025: Turnover Data, Japan," page 5, the "Total" row of Table 1 "Breakdown by Counterparty and Instrument" in Annex 1 (in billions of US dollars). ↩