The components of FX option pricing

What is an FX option?

An FX option is a contract that confers on the holder the right (but not the obligation) to exchange an amount of one currency for another at a pre-agreed rate (strike rate) on or before a pre-agreed date.

An FX option has four primary economic terms: the currency pair, the amount covered (the notional), the duration of the option (the term), and the level of protection (the strike rate).

• Currency pair: This is the underlying currency that the option is hedging. The holder of the option elects one currency to sell (put currency) and one currency to buy (call currency).
• Notional: The notional is the amount covered by the option. The call (or the put) currency can be fixed and specified.
• Term: The term of the option is the length of time before the option expires. The holder of the option has the right, but not the obligation, to exchange an amount of one currency for another at the strike rate at expiry. Delivery of the amounts will usually be two days after expiry.
• Strike rate: The strike rate is the level of protection. It is the pre-agreed rate that the option holder has the right to exchange the currency. This is often referred to as a measurement of the spot rate or of the forward rate. If it is exactly at the spot rate, it is called ATMS (at the money spot). If it is the forward rate for the same date as the expiration date, it is called ATMF (at the money forward). It can also be X% OTMS (out of the money spot) or OTMF (out of the money forward).

How does an FX option work?

Let’s consider an example where one wants to exchange EUR 50M to USD in two years’ time, and the protection level required is the current spot rate. One can buy an option with the following details:

• Put EUR 50M, call USD, at a strike of EUR-USD 1.18 (at the money spot) for an expiry of two years

On the expiry date, the strike rate will be compared with the prevailing spot rate. If the strike rate is more favorable to the option holder, then the option holder will convert at the strike rate. Let’s say EUR-USD is 1.17 in two years’ time; 1.18 is a more favorable rate, so the option holder will convert the EUR 50M into USD using 1.18. Compared with the spot level 1.17, the payout of the option (which is the value of the option at expiry) is calculated as the difference between the amount one is able to convert in the market using the prevailing spot rate and the amount one is able to convert by exercising the option.

• Converting by exercising the option: EUR 50M * 1.18 = USD 59M
• Converting in the market using spot: EUR 50M * 1.17 = USD 58.5M

The option payout is the difference between the two: USD 59M – USD 58.5M = USD 0.5M. If the prevailing spot rate is more favourable to the holder than the option strike, then the payout is zero. The option expires worthless and the holder will simply transact at the prevailing spot.

How is the cost of an FX option determined?

An FX option is purchased with a premium, which is usually paid upfront. The premium has two components: the intrinsic value and the time value.

FX option premium = intrinsic value + time value

Intrinsic value: The intrinsic value of the option is the difference between the amounts converted using the strike rate and the forward rate. It assumes that the option is exercised on the day of calculation and the payout is calculated as the intrinsic value.

Intrinsic value = notional * (strike – current forward rate)

For example, let’s assume the current forward rate is 1.17 and we are the holder of this option: Put EUR 50M, call USD, at a strike of EUR-USD 1.18 for expiry 15 November 2022.

It is the same calculation as the payout in the previous section: Intrinsic value = EUR 50M * (1.18–1.17) = USD 0.5M.

Time value: Time value is the monetary value associated with the amount of time remaining before expiry. It’s more complex to directly say what the calculation is, but it is impacted by a few factors including term, strike rate, volatility, and exercise style.

• Term: The longer the term, the greater that time value will be. This is because there is a greater uncertainty about whether an option will be exercised by the holder and the magnitude of how the strike rate will differ from market levels at the time of expiry.
• Strike rate: The strike rate determines the level of protection. The more favorable the strike rate is, the greater the time value will be. If the strike rate is more favorable to the option holder, there is a higher likelihood for the option to have a positive payout.
• Volatility: Volatility is the primary driver for time value; the higher the volatility in the currency pair, the greater the time value will be. Volatility is a measure of the speed and magnitude of movement for the underlying currencies. High volatility means that there is a higher probability for the option to be in the money and to have a positive payout at expiry. Volatility is not linear. Increasing the FX rate does not necessarily increase volatility proportionally. Volatility is also not symmetrical for the same currency pair. An option putting USD and calling EUR often sees different volatility when compared to an option calling USD and putting EUR with the same structure.
• Exercise style: There are a few exercise styles for options: European (only one exercise at expiry); American (exercise any time at or before expiry), and Bermudan (exercise at multiple pre-specified dates). In general, the more “optionality” there is, the greater the time value. An American style option costs at least as much as a European style option with the same structure. Any difference in pricing is determined by the likelihood of an early exercise.

The pricing of FX options depends on a number of moving elements and is particularly sensitive to live market levels, including spot rates and volatility measures. Many companies and funds partner with Chatham for this process of determining an option strategy to hedge FX risk. Chatham can source competitive counterparties, assist with live execution, and provide daily valuations for the duration of the option term.