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I hope this is a simple question but I just wanted to get confirmation and also the intuition behind it.

I know the put call symmetry and I often see it expressed as: Call(S, K) = Put(K, S) = K/S Put(S, S^2/K) where S is the spot and K is the strike.

I was wondering if it is the same from the perspective of Puts, i.e.: Put(S, K) = Call(K, S) = K/S Call(S, S^2/K)

Thank you in advance for any help

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  • $\begingroup$ Just mechanically interchanging S and K in the first part I get that Call(K,S) = Put(S,K) = S/K Put(K,K^2/S) The last term could be rewritten as S/K Call(K^2/S, K) $\endgroup$ – Alex C May 1 at 2:30

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