# FOREX Ladder Options

The purchaser of an option contract has the right, but not obligation, to buy (via a call option) or sell (via a put option) a stated asset (the underlying) at a stated price (the strike price) on or before the option expiration date. Many options are standardized and are traded on exchanges; they are called "vanilla" options. More elaborate options, known as exotics, are handcrafted and are sold over-the-counter in an arranged deal between two specific counterparties. A FOREX ladder option is an exotic option that confers certain extra benefits upon the option holder. Exotic options such as the ladder are more expensive to purchase because of their additional benefits.

## FOREX Pricing

The underlying asset of a FOREX ladder option is a currency pair. Currencies always trade in pairs, such as EUR/USD--the euro/U.S. dollar pair. The numerator is the basis currency, which is the currency being bought. The denominator, or quote currency, is being sold. For example, an exchange ratio of 1:1.3380 means that $1.3380 can be sold to buy one euro. The price is always carried to four decimal places, called a pip for percentage-in-point. A call option with a strike price of 1.3380 would be termed at-the-money because the strike is equal to the current price. A higher strike would be out-of-the-money; a lower strike would be in-the-money. Reverse these definitions for put options.

## Vanilla Call

In our example, we have a three-month EUR/USD call option with a strike price of 1.3400. The underlying asset is a standard EUR/USD lot of $100,000. You pay a premium of 11 pips to buy the call, which is .0011 * $100,000, or $110 dollars. The price of an option derives from a combination of its intrinsic value (the current price minus the strike price for a call; reversed for a put) and its time value--longer expirations have higher time values, since this gives an option more opportunities to go into-the-money. Should the current EUR/USD price fail to reach 1.3400, the option will expire worthlessly. The break-even price is 1.3411, or 11 pips above the strike price, equal to the initial premium.

## Ladder Call

A ladder call option is like a vanilla call option except that it has a series of "rungs", or intermediate strike prices. A ladder version of our example would have strikes at 1.3380, 1.3385, 1.3390, 1.3395, and 1.3400. The unique characteristic of the ladder call is that as current prices rise above a strike rung, the rung becomes a floor on the call's value. If the EUR/USD price initially rose to 1.3392, the 1.3390 rung would be triggered and the purchaser will have locked in a gain of 5 pips. As prices continued to rise, each subsequent rung would secure another 5 pips of guaranteed gain, independent of any decline in the currency pair price.

## Profit Calculation

The price lock-in feature of a ladder option comes at a cost: a premium higher than the vanilla call's 11 pips. The determination of the actual premium requires a sophisticated pricing model--we will stipulate a premium of 20 pips. The call holder will just break even if the EUR/USD price rises to 1.3400, because the 20 pips of locked-in profit matches the 20 pip premium. Any currency-pair price rise above 1.3400 is a pip-for-pip profit to the call holder. If the option expires at 1.3417, the buyer nets a 17 pip profit (37 pips proceeds minus 20 pips cost) which equals .0017 * $100,000, or $170. The return on the trade is 17/20, or 85 percent.