The word option is derived from the Latin word “optio”, which we can loosely translate as “the right to choose”. The characteristic of the option embodies the right to choose. The ownership of an option conveys the right but not the obligation to buy (or sell, depending on option type) a commodity at a given price within a certain period or at a certain point in the future.
Because of this lopsided payoff characteristic, options are sometimes referred to as asymmetrical instruments.
Calls & Puts
A call option gives the buyer of the option the right (but not the obligation) to buy a set quantity of the underlying instrument at a predetermined price (the “strike” price), at a specific date (European style option), or at any time during a specific period (American style option). For this right the buyer pays a premium to the seller. Because no obligation to exercise an option exists for the buyer (holder), the buyer’s downside risk, in the event of an adverse price movement, is limited to the premium paid. This limited obligation creates the asymmetry mentioned in the introduction.
A put option gives the buyer of the option the right (but not the obligation) to sell a set quantity of the underlying instrument at a predetermined price. The put option is the opposite of the call option.
Because currency trading always involves buying one currency and selling the other one, a currency option is always a call on currency A and a put on currency B. Both descriptions are correct. In order to avoid misunderstandings, we always say “USD call” or “EUR put”, as opposed to simply “Call” or “Put”.
A call is the equivalent of a long forward position with a loss insurance policy.
A put is the equivalent of a short forward position with a loss insurance policy.
The Value of an Option
Some of the most seemingly basic concepts relating to options are not so basic. One such concept is whether an option is deemed to be “in-the-money” (ITM). At first blush, this concept seems simple enough. The price at which an option can be exercised is called the strike price. In the case of a call (which is the right to purchase an asset), the option is “in-the-money” if the strike price is cheaper than the price at which the asset can be purchased in the open market. In the case of a put, the option is “in-the-money” if the strike price is more expensive than the price at which the asset can be sold in the open market. In the reverse situations, the option is called “out-of-the-money” (OTM). When the strike price and the asset price are the same, the option is called “at-the-money” (ATM).
This all seems rather simple, but there is one twist: for measuring the price for such open market purchases and sales, the relevant value date is the same as the settlement date for exercise under the option. Thus, if USD-CHF call option (a call on the underlying USD and a put on the CHF) is struck at 1.08, it would be in-the-money if the forward price for USD-CHF (on the settlement date for the option exercise) is greater than 1.08. In the case of a European option (see below), this date is the spot date for the exercise date (i.e., generally two business days following the exercise, or maturity, date). While the forward price is the relevant price at which options are technically viewed as “at-the-money”, sometimes people will also refer to an option struck at spot and use the shorthand of referring to that sort of option as being “at-the-money-spot”.
The value of an option consists of “intrinsic value” and “time value”. The intrinsic value of an option is easily measured: it is the amount that the option is “in-the-money”. Out-of-the-money and at-the-money options have no intrinsic value.
Time Value + Intrinsic Value = Option Price
Example
A call on the USD / put on the CHF, with a strike of 1.08 is “ITM” and has an intrinsic value of 1% if the outright forward is trading at 1.0908 (i.e., 1% above the strike), not accounting for the cost of carry. If the outright forward trades at 1.08 (ATM) or below (OTM), the intrinsic value of the USD call is zero.
Put options have limited gain/loss in the event that the underlying goes to zero. However, for currencies this is not necessarily true, since a put on Currency A is a call on Currency B. Put Currency A going to zero is equivalent to call Currency B going to infinity. If profit/loss are computed in terms of (put) currency A, then the loss can indeed be infinite.
The time value of an option is the difference between the intrinsic value of the option and its actual price. ATM and OTM option premiums consist entirely of time value.
The time value, as the name implies, is a function of time to expiration, but also of “implied volatility” or the expected future price range – the future probability of prices. Assume that we own a USD call, strike 1.80 for 1 month. Spot is currently 1.80 and forwards are zero. For simplicity’s sake let us assume that we have only a limited number of 5 possible spot prices at expiration: 1.74, 1.77, 1.80, 1.83, 1.86. The probabilities of these outcomes are illustrated in the below graph.
Probability of Outcome
We can calculate the weighted sum of these probable outcomes. The weighted probable outcome is for spot to be at 1.80, but because of the insurance feature of the option, we will incur no loss if spot ends up below 1.80. We can now weigh the potential profit according to the probabilities, and sum the numbers. The result is 0.0105 CHF per 1$. Since the option has no intrinsic value, and we assume interest rates are zero, this is the fair value of the option insurance, or the time value of the option.
Notice that “Time Value” decreases in importance, as the option moves far in-the-money or far out-of-the-money. Time Value, unlike Intrinsic Value (if the option is ITM), is not a linear function of the spot price.
Option Basics
Linear Mode
