Interpreting FX Options as Calls or Puts on Either Currency

Summary

The document explains that an FX option can be described from either currency’s perspective. An option to exchange a fixed amount of one currency for another can be framed as a call on the currency being acquired or a put on the currency being sold. The answer clarifies the relationship by expressing the same exchange in equivalent units, rather than simply inverting the quoted exchange rate and reusing the original contract terms.

In the example, the option to obtain a specified amount of USD in exchange for AUD is equivalent to the right to sell a specified amount of AUD for USD at the corresponding strike. The crucial point is that notional amount and strike must be translated together when changing the underlying currency. The explanation is limited to interpreting the contract’s payoff and quote conventions; it does not cover option valuation, premiums, or how market conventions may specify FX option notionals.

Key ideas

• An FX option can be viewed as a call on one currency or a put on the other.
• Changing the underlying currency requires translating both the notional and strike.
• Equivalent descriptions follow from the same right to exchange fixed currency amounts.
• The payoff interpretation alone does not determine an option’s market value.

Tags

# In FX markets, option can be expressed as either call or put. Explain


# In FX markets, option can be expressed as either call or put. Explain












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.

## Answer by Kurt G. (score 1, accepted)

https://quant.stackexchange.com/a/68925

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.