## Fx option payoff formula

- Call Option Payoff Diagram, Formula and Logic - Macroption
- FX Currency Options - The USD JPY FX options convention

When and why should I use currency options?

Your risk is limited to the price of the option.

Traders trade market volatility, or they trade without classic stop-loss strategies.

Portfolio managers and businesses hedge Forex risks.

## Call Option Payoff Diagram, Formula and Logic - Macroption

How does an FX Option work?

The option price consists of intrinsic and time value.

There are FX Call and FX Put Options for both market directions.

American options can be exercised anytime on or before the date of expiration.

European options can only be exercised on the date of expiration.

### FX Currency Options - The USD JPY FX options convention

Hence, a Forex call option has intrinsic value if the FX spot price is above its strike price. A Forex put option has intrinsic value if the FX spot price is below its strike price.

A currency option (also known as a forex option) is a contract that gives the buyer the right, but not the obligation, to buy or sell a certain currency at a specified exchange rate on or before a specified date. For this right, a premium is paid to the seller.

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The intrinsic value is the amount of money we could realize through exercising our option, under the assumption that the FX spot rate will equal the current rate on the expiration date. The reason is that the time value will always be zero when the currency option expires.

Besides the strike price, another important point on the payoff diagram is the break-even point, which is the underlying price where the position turns from losing to profitable (or vice-versa). On the chart it is the point where the profit/loss line crosses the zero line and you can see it’s somewhere between 87 and 88 in our example.

The investor sells a digital option for gold at a $6,755 strike price with expiry at the end of the day and will be paid $65 at expiry if correct. Since each of these digital options have a maximum value of $655, the premium paid in the event of a loss will be $85 or ($655 - $65).

For business school students taking the treasury product exam or preparing for a trading desk interview, the USD JPY pair is particularly troublesome. Here is a list of common errors and challenges side by side with four simple examples for options on the USD JPY pair that we hope would clear the frustration around this pair.

Exercise

Exercising the option means using the right that has been granted by buying the option. If the buyer decides to exercise the option, then the seller will be informed, and the guaranteed FX transaction will happen.

One other thing you may want to calculate is the exact underlying price where your long call position starts to be profitable. In other words, the point where the payoff chart crosses the zero line, or where the total P/L (which we have calculated above) equals zero – the break-even point.

It is very easy to calculate the payoff in Excel. The key part is the MAX function the rest is basic arithmetics. You can see all the formulas in the screenshot below.

Expiry Date

The expiry date (expiration date) is the last date at which the option may be exercised. After this date, the option contract expires.

Additional types of exotic options may attach the payoff to more than the value of the underlying instrument at maturity, including but not limited to characteristics such as at its value on specific moments in time such as an Asian option , a barrier option , a binary option, a digital option , or a lookback option.

Call options are bought when the price of the underlying is expected to rise. Put options are bought when the underlying s price is expected to fall.

Consider a 7-day at-the-money (ATM) European call option on the US dollars, to buy USD dollars for Japanese Yen. Suppose that the current USD-YEN spot exchange rate is , the exercise price is 665, the risk free rate in the United States is % per annum and the risk free rate in Japan is -% per annum. ATM implied volatility in the USD-YEN rate is %. The notional amount is USD 6555.

The original term sheet speaks of an exchange of currency at a pre-defined strike exchange rate. In particular, for a call option on USD that is exercised, the customer will buy USD 6555 at the exchange rate of 665. This means he will sell JPY 665,555. In terms of equivalency (where a call option on USD is the same as a put option on JPY), this means that an exercised put option on JPY will see him selling sell JPY 665,555 at the exchange rate of 6/665 to fund a USD 6555 purchase.

Unlike vanilla options, selling a digital option does not mean the trader is writing an option , which involves the seller or writer being paid a fee for allowing the buyer to exercise the option. In most cases, investors who sell traditional options use them as an income strategy and hope the option will not be exercised so they can keep the premium.

After determining the appropriate currency convention to use in the option pricing formula, another point of confusion is with regard to the risk free rates. In particular, which currency’s risk free rate in the exchange rate pair is to be considered the domestic currency risk free rate, r, and which the foreign currency risk free rate, r f.

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