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I am a bit lost with understanding the naming used for holding positions in the currency options and their payoffs.

If I want to buy the European option with an amount of x USD (EUR put/ USD call), what is the position I should hold? Is it a long call or a long put?

I would say a long call but then I am confused about the payoff. The rule for exercise at expiration with European options is that the long call is in-the-money:

  • Strike price < Spot price at maturity

How this translates into this situation:

LONG CALL

My strike price = 1.25 EUR/USD

Spot price at maturity = 1.3 EUR/USD

I want to buy 1000 USD.

In this situation, the rule for long call exercise does not make sense (Strike price < Spot price at maturity) because if I buy 1000 USD then at the strike price it is equal to (1000/1.25) = 800 EUR and at the spot rate it is equal to (1000/1.3) 770. This means that it is better NOT to exercise the option when the strike price < spot price and it is better to buy at the spot.

Am I missing something? Why the rule says that the strike price should be less than the spot rate at maturity to exercise long call??

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The given answer by Jake Freeman is missing the point.

FX is quoted as CCY1CCY2 (e.g. EURUSD) where it shows the amount of CCY2 needed to buy/sell 1 unit of CCY1. In terms of options, the standard Black Scholes model (called Garman Kohlhagen in FX) has Notional in CCY1, but price in CCY2. The call and put position refers to CCY1. A EUR Call is equal to a USD Put.

Hence, if you want a Put on EUR you just need to buy a put option. However, you stated you want the Notional in USD. This requires some tweaking in the calculation formula. If you do not compute it yourself, and just care about directions, you can simply select the notional to be in USD. The screenshots below are from Bloomberg's FX option pricer OVML. It shows clearly that a EUR Put is identical to a USD Call.

enter image description here

In your example, if Spot is 1.3 and your EUR Put Strike is set at 1.25, you indeed would sell EUR at market price to buy 1000 USD and not use the option. You also correctly stated that, if you sell at market, you only need ~769.23 EUR. If you were to use your option, you would need 800 EUR. In the standard Black Scholes world, this is a long put (which is by default on EUR).

You can look here if you know some basic coding and are interested to compute the values yourself.

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FOREX Options only trade on one pair. For EUR/USD u can only make options EUR/USD. You can exercise a long call at any given price at maturity. It only makes sense, however, to exercise when you would make money.

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  • 2
    My question has nothing to do with your answer.
    – Dozens
    Commented May 31, 2019 at 9:09
  • Your question is why do you need the strike to be below the spot rate
    – Jake Freeman
    Commented May 31, 2019 at 12:44

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