If you’re thinking about trading FX options or have begun trading already, you probably have at least a basic grasp or intuitive under- standing of some of the relation- ships at work. As you trade though, you may discover that an intuitive understanding alone is not sufficient to guide all your trading choices and decisions.

This tutorial and the accompanying FX options simulator build upon your intuitive understanding. They show you how to think about FX options in more sophisticated ways and how to make trading decisions more systematically.

For instance, you probably know that, if you think the price of a currency is likely to go up over a given time horizon, then what you want to do is buy a call option on that currency. Most likely, you will want the call to have a time to expiration roughly equal to the time horizon over which you have confidence in your forecast.

You know that, if, at the time of the option’s expiration, the spot price of the underlying currency is above the call’s strike price, then you get a payoff. The higher the spot price above the strike price, the greater your payoff. If your payoff is greater than the price you paid for the call, then you make a profit. But, when you go to buy a call, how do you pick the strike price?

For a call, the lower the strike price, the greater the probability that you will get a payoff, but also the more expensive the call will be. If the payoff is less than the amount you paid for the option, then you have a loss.

As an investor or trader, you wish you could have a high probability of profit and a high expected return. But with options, up to a point, you make a tradeoff between probability of profit and expected return. .

To decide which option to buy, you may want to calculate probability of profit and expected return for different strike prices and pick the strike price that gives you the tradeoff that works best for you.

With the simulator, you enter the spot price of the underlying currency, your forecast for the currency and your cost of capital. You enter an option’s time to expiration, its strike price and the dealer’s ask price.

Given these parameter values, the simulator calculates the option’s probability of profit and expected return. You can make these calculations for different strike prices. You can pick the strike price that gives you the tradeoff you want between probability of profit and expected return.

Or, you can enter the probability of profit you want. The simulator will give you the strike price that, ideally, will produce it.

Your forecast for an underlying currency implies a value for an option with a given time to expiration and strike price. Going in the other direction, a dealer’s bid or ask price for an option implies a forecast for the underlying.

With the simulator, you can draw your forecast for the underlying currency. You can draw the forecast that the dealer’s bid or ask price implies. You can compare the two.

If the two forecasts disagree and yours better captures market dynamics, you have an opportunity to profit from an option trade or trades. Which trades to make depends on how your forecast disagrees with the implied forecast. The tutorial looks at the seven ways in which your and a dealer’s forecasts can disagree. It suggests option trades for each one.

Your forecast for the underlying currency

Express your forecast for an underlying currency as an end-of-period price range.

The standard model for valuing FX options assumes that currency prices evolve through a process of geometric Brownian motion.

Every financial forecast is a probability distribution.

The standard model for valuing FX options assumes potential currency price-path outcomes to be normally distributed.

From your forecast for the underlying currency, you can simulate potential option payoffs, profits and returns.

To find your value for an option, evaluate your forecast’s potential price-path outcomes against the option’s strike price.

From your forecast and an option’s strike price and price, you can calculate an option’s probability of profit and expected return.

With the simulator, you can enter the probability of profit you want on an option purchase; the simulator will give you the strike price that has that probability of profit.

The dealer’s non-arbitrage,
risk-neutral currency forecast

From the midpoint between a dealer’s bid and ask prices for an option, we can extract the forecast for the underlying currency that the price implies.

The dealer’s forecast is a non-arbitrage, risk-neutral forecast.

If a currency price had zero volatility, it would evolve toward its future price in a straight line. Options would serve no purpose.

With volatility, to prevent arbitrage, the average return of an implied currency forecast must equal the domestic risk-free rate minus the foreign risk-free rate.

In a dealer’s forecast, the average growth rate of the foreign currency is equal to the domestic risk-free rate minus the foreign risk-free rate.

When we evaluate a risk-neutral forecast against an option’s strike price, we get the option’s risk-neutral vlaue.

The standard formula for valuing FX options evaluates a risk-neutral forecast against a strike price. The formula gives the same answer as (but more precisely than) our step-by-step evaluation.

For a risk-neutral forecast, the expected return on any option equals the domestic risk-free rate.

Dealers are market makers. They calculate an option’s risk-neutral, non-arbitrage value. They set an ask price above that value and a bid price below. They make profits on the bid-ask spread.

Failure of currency markets to conform exactly to the standard model produces a volatility smile. Smile means dealers’ option prices for different strike prices may give different implied volatilities.

Exploit differences between
your forecast and the dealer’s

When you buy a stock, bond or currency, you buy the asset’s entire probability distribution. When you buy an option, you buy only part of an asset’s probability distribution.

If your forecast disagrees with the dealer’s forecast, then, according to your forecast, the dealer’s forecast overvalues part of your forecast’s probability distribution and undervalues other parts. You can buy from the dealer the undervalued parts and sell to him the overvalued parts.

If you disagree with the forecasts that a dealer’s prices imply and your forecast better captures market dynamics, then you can buy options that will leverage your expected return.

Your forecast can disagree with the forecasts that a dealer’s prices imply in seven different ways.

Which trades to make depends on how your forecast disagrees with the forecasts that a dealer’s prices imply.

Implied forecast’s low price is
too low.
Implied forecast’s high price is
too low.

Implied forecast’s low price is
too low.
Implied forecast’s high price is
just right.

Implied forecast’s low price is
too low.
Implied forecast’s high price is
too high.

Implied forecast’s low price is
just right.
Implied forecast’s high price is
too low.

Implied forecast’s low price is
just right.
Implied forecast’s high price is
too high.

Implied forecast’s low price is
too high.
Implied forecast’s high price is
too low.

Implied forecast’s low price is
too high.
Implied forecast’s high price is
too high.

Hold position to maturity or bail out before?

Everything changes.

For an open option position, plot the price path of the underlying currency that will make the option break even.

For an open option position, calculate probability of profit and expected return. If you don’t like the odds, close the position. Book your profit or take your loss.

If your forecast doesn’t pan out, what’s the worst that could happen?

When you sell one option, you may want to buy another that limits your risk exposure.

This tutorial and simulator work with one option at a time. To manage risk exposures of multiple positions, you need a system that tracks how your different positions interact with one another.

All models are wrong. Some are useful.

Currency price process isn’t really geometric Brownian motion.

Currency price-path outcomes aren’t really normal distributions.

Expected volatility may not remain constant over an option’s time to expiration.

Dealers’ prices for calls and puts may not give same implied volatilities.

The standard model may be wrongish, but you can understand it. More sophisticated models are harder to understand and much more difficult to calibrate to the market.

May FX Options Made Easy be not the end, but the beginning of your study of FX options trading.

From dealer's bid, ask or mid-point price, extract implied risk-neutral,
non-arbitrage forecast for underlying foreign currency.

From an end-of-period price range that you specify, quantify your forecast for a foreign currency.

From your forecast and from the dealer's implied forecast, simulate potential currency price paths and option payoffs.

For your forecast and for dealer's implied forecast, draw price-path probability bands. Divide bands into either standard deviations or deciles.

For your forecast and for dealer's implied forecast, draw end-of-period probability distributions. Divide probability distributions
into either standard deviations or deciles.

From your forecast, calculate a call or put's cumulative probability-weighted present value, expected return and probability of profit.

Compare your forecast with the dealer's implied forecast. Identify options that will maximize your expected return. Pick the options that give you the tradeoff you want between expected return and probability of profit.