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For example, if option contract has condition: $AUDUSD = 0.8$ at the maturity date, and current exchange rate is $1 AUD = 0.75 USD$.

For this option, it could be considered a call option on $USD$, and put option on $AUD$ since $AUDUSD$ means that $AUD$ is sold 1 to buy $USD$ 0.8.

For the call option perspective, I get that strike price is $0.8$.

What I don't understand is the strike and spot price of the put option.

Why is it that spot for the put is 1, not 1.33( = 1/0.75), and strike is 0.9375(0.75/0.8), not 1.25( = 1/0.8) ?

Maybe I'm missing some basic concept about Fx or put options?

Thanks in advance.

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    $\begingroup$ “spot for the put is 1”. Where do you get this from? $\endgroup$
    – dm63
    Nov 27 '21 at 16:56
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    $\begingroup$ You might want to clarify the question as your terminology is non-standard and confusing. Options have expiry dates, not maturity dates, and what you refer to as a "condition" is - I think - the strike price. I assume you're referring to an OTM call on AUD which is a put on USD. You don't start quoting USDAUD just to describe a put on AUD. $\endgroup$
    – user42108
    Nov 27 '21 at 17:31
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    $\begingroup$ This answer offers a complete Put on JPY = Call on USD calculation. Strike does not change. $\endgroup$
    – AKdemy
    Nov 27 '21 at 17:59
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The option allows to

  • buy $1$ USD for $1/0.8$ AUD, or equivalently,
  • buy $0.8$ USD for $1$ AUD.

Since buying USD is equivalent here to selling AUD this same option allows to

  • sell $1$ AUD for $0.8$ USD (put on AUD with strike $0.8$).

To summarize: the call option on $0.8$ USD with strike $1/0.8$ is the same as a put option on $1$ AUD with strike $0.8$

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