The key difference between a call option written on the USD cost of the AUD and a put option written on the AUD cost of the USD is the standard deviation estimate.

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One important characteristic of currency options is the symmetry between a call option written on the AUD cost of USD and a put option written on the USD cost of AUD.The key difference between the two is the change in standard deviation estimate as the standard deviation of the AUD cost of USD is not the same as the standard deviation of the USD cost of AUD.Once the standard deviation is correctly estimated,these two option premiums should be identical.

The Key Difference Between a Call Option Written on the USD