Vanilla Call and Put Options

Vanilla FX call option contracts give the right-to-buy spot on a specific date in the future while vanilla FX put option contracts give the right-to-sell spot on a specific date in the future. The term vanilla is used because calls and puts are the standard contract in FX derivatives. The vast majority of derivative transactions executed by an FX derivatives trading desk are vanilla contracts as opposed to exotic contracts. Exotic FX derivatives (covered in Part IV) have additional features (e.g., more complex payoffs, barriers, averages).

To understand how call and put options work, forget FX for the moment and think about buying and selling apples (not Apple Inc. stock, but literally the green round things you eat). Apples currently cost 10p each. I know that I will need to buy 100 apples in one month's time. If I simply wait one month and then buy the apples, perhaps the prevailing price will be 5p and hence I can buy the apples cheaper than they currently are or perhaps the price will be 15p and hence more expensive or perhaps they will cost 10p, 1p, or 999p. The point is that there is uncertainty about how much the apples will cost and this uncertainty makes planning for the future of my fledgling apple juice company more difficult. Call and put options allow this uncertainty to be controlled.

One possible contract that could be purchased to control the risk is a one-month (1mth) call option with a strike of 10p and a notional of 100 apples. Note the different elements within the contract: the date in the future at which I want to complete the transaction (maturity: one month), the direction (I want to buy apples; therefore, I purchase a call option), the level at which I want to transact (strike: 10p) and the amount I want to transact (notional: 100 apples). After buying this call option, one month hence, at the maturity of the contract, if the price of apples is above the strike (e.g., at 15p) I will exercise the call option I bought and buy 100 apples at 10p from the seller (also known as the writer) of the option contract. Alternatively, if the price of apples is below the strike (e.g., at 5p), I don't want or need to use my right to buy them at 10p; hence the call option contract expires. Instead I will buy 100 apples directly in the market at the lower rate.

Therefore, by buying the call option, the worst-case purchasing rate is known; under no circumstances will I need to buy 100 apples in one month at a rate higher than 10p (the strike). This reduction in uncertainty comes at a cost: the premium paid upfront to purchase the call option. It is not hard to imagine that the premium of the call option will depend on the details of the contract: How long it lasts, how many apples it covers, the transaction level, plus crucially the volatility of the price of apples will be a key factor. The more volatile the price of apples, the more the call option will cost.

Exhibit 2.1 shows the P&L profile from this call option at maturity, presented in familiar hockey-stick diagram terms but without the initial premium included.

At the option maturity, if the price of apples is below the strike (10p), the call option has no value because the underlying can be bought cheaper in the market. If the price of apples is above the strike at maturity, the call option value rises linearly with the value of the underlying.

Mathematically, the P&L at maturity from this call option is:

where is expressed in terms of number of apples, is the price of apples at the option maturity, and is the strike. Often is written .

It is worth noting that the P&L at maturity from the contract depends only on the price of apples at the moment the option contract matures; the path taken to get there is irrelevant.

Put options are the right-to-sell the underlying. This can be conceptually tricky to grasp at first—buying the right to sell. Imagine you own a forest of apple trees. You know that by the end of August you will harvest at least 1,000 apples, which you will then want to sell. Again, uncertainty arises from the fact that the future price of apples is unknown. To control this uncertainty, a put option maturing on August 31 could be bought with a notional of 1,000 apples and a strike of 10p.

This time, at the option maturity, if the price of apples is below the strike (e.g., at 5p), the put option will be exercised and 1,000 apples will be sold at 10p to the option seller. Alternatively, if the price of apples is above the strike (e.g., at 15p), the put option will expire and 1,000 apples can instead be sold in the market at a higher rate.

By buying the put option, the worst-case selling rate is known; under no circumstances will I need to sell 1,000 apples at a rate lower than 10p (the strike) at the end of August. The cost of buying this derivative contract will depend on the exact contract details, plus, again, the more volatile the price of apples, the more the option will cost. Exhibit 2.2 shows the P&L profile from this put option at maturity.

Mathematically, the P&L at maturity from this put option is:

Bringing these concepts into FX world, the underlying changes from the price of apples to an FX spot rate. At the option maturity, the prevailing FX spot rate will be compared to the strike to determine whether a vanilla option will be exercised or expired.

There are actually two main kinds of vanilla option:

1. European vanilla options can be exercised only at the option maturity.
2. American vanilla options can be exercised at any time before the option maturity.

European vanilla options are the standard product in the FX derivatives market because they are easier to risk manage and mathematically simpler to value. Henceforth, any mention of a vanilla option means a European-style contract. American vanilla options are covered in Chapter 27.

The following details are required to describe a vanilla FX option contract:

1. Currency pair The spot FX rate in this currency pair is the reference rate against which the value of the vanilla option will be calculated at maturity.
2. Call or put (call = right-to-buy/put = right-to-sell): FX transactions exchange two currencies: one that is bought and one that is sold. Therefore, a vanilla option in a particular currency pair is simultaneously a right-to-buy one currency and a right-to-sell the other. Therefore, vanilla options are simultaneously a call on CCY1 and a put on CCY2 or vice-versa. Most often only the CCY1 direction is specified when describing the contract, so, for example, a EUR/USD call option is actually a EUR call and a USD put.
3. Maturity/expiry: The date on which the owner of the option decides whether to exercise their option or let it expire. There is actually a third option to partially exercise the option, which is explored in Chapter 9.

4. Cut: The exact time on the expiry date at which the option matures.

   The two most common cuts in G10 currency pairs are:

   • New York (NY): 10 a.m. New York time, which is usually 3 p.m. London time.
   • Tokyo (TOK): 3 p.m. Tokyo time, which is 6 a.m. or 7 a.m. London time, depending on the time of year.

   

5. Strike: The rate at which the owner of the option has the right to exchange CCY1 and CCY2 at maturity.
6. Notional: The amount of cash (usually expressed in CCY1 terms) that can be exchanged at maturity. Vanilla option notionals can be converted between CCY1 and CCY2 terms using the strike as shown in Exhibit 2.3 since the strike is the level at which CCY1 and CCY2 are potentially exchanged at maturity.

Mathematically, the P&L at maturity from a long (bought) CCY1 call option is:

where is the spot FX rate at the option maturity and is the strike. The CCY1 call P&L at maturity is the same as a long FX position (to the maturity date, i.e. a forward) above the strike. Exhibit 2.4 shows the P&L at maturity from a long USD/CAD call option (USD call/CAD put).

Likewise, the P&L at maturity from a long (bought) CCY1 put option is:

The CCY1 put P&L at maturity is the same as a short FX position below the strike. Exhibit 2.5 shows the P&L at maturity from a long USD/CAD put option (USD put/CAD call).

Exhibit 2.6 shows a USD/JPY vanilla contract in an FX derivatives pricing tool. Traders use systems like this to price vanilla option contracts.

Within the pricing tool, the horizon is the current date (i.e., today). On the expiry date (Nov. 20, 2013) at 10 a.m. NY time (since the option is priced to NY cut), the owner (buyer) of this European-style vanilla option will contact the writer (seller) of the option to inform them if they want to exercise the option.

If the spot rate at maturity is above the strike (80.00), the option is said to be in-the-money (ITM). In this case the option will be exercised because the option gives its owner the right to transact at a better rate than the spot level. If the option is exercised, on the delivery date (Nov. 22, 2013; the delivery date is calculated from the expiry date in the same way that the spot date is calculated from the horizon—see Chapter 10 for more information on tenor calculations), the option owner will get longer USD5m versus shorter JPY400m while the option writer will get the opposite position.

If the spot rate at maturity is below the strike (80.00), the option is said to be out-of-the-money (OTM). The option owner should let the option expire because USD/JPY spot can be bought more cheaply in the market.

Note that for a put option with all other contract details the same, the ITM and OTM sides flip: the ITM side is below the strike and the OTM side is above the strike.

Within the pricing tool, both volatility and premium prices are shown for the contract. Some market participants want prices quoted in volatility terms while others want prices quoted in premium terms. The Black-Scholes formula provides the link between volatility and premium. The formula takes as inputs the vanilla option contract details: maturity, option type (call or put), strike, plus market data: current spot, current forward/interest rates to the option maturity. The final input is volatility and the Black-Scholes formula can then be used to calculate the option premium. In Exhibit 2.6, a two-way volatility (explained in Chapter 3) is given and the Black-Scholes formula is used to calculate an equivalent two-way premium. It may seem strange that a price would be quoted in volatility terms but this is exactly how the FX derivatives market works. The essence of an FX derivative trader's job is to buy and sell exposure to FX volatility.

Practical Aspects of the FX Derivatives Market

FX derivatives trading volumes are roughly 5% of total foreign exchange trading volumes, equating to hundreds of billions of U.S. dollars' worth of transactions every day. Currency pairs that have higher trading volumes in their spot, forward, and FX swap markets tend to also have higher trading volumes in their FX derivatives markets.

The majority of FX derivatives trading occurs in contracts with maturities of one year and under. However, in some currency pairs long-dated contracts are traded—sometimes out to ten years or even longer.

Vanilla options in G10 currency pairs are usually physically delivered, meaning that at maturity, if the option is exercised, an exchange of cash flows (i.e., an FX spot trade) occurs.

In some emerging market currency pairs, vanilla options are cash settled, meaning that at maturity a fix is used to determine a settlement amount that is paid as a single (usually USD) cash flow. In G10 currency pairs it is also possible to use a fix to settle derivative contracts but this is less common.