Put-Call Symmetry and the Corresponding Put Option Identity

Summary

The document asks whether a stated put-call symmetry for calls has a corresponding form when starting from a put. It gives the call-side relationships in terms of spot and strike, then proposes swapping the call and put roles and exchanging the relevant spot and strike arguments. The subject is a symmetry identity for option prices, rather than a trading strategy or empirical result.

No answer, derivation, assumptions, or examples are included in the supplied text. In particular, it does not establish when the displayed relationships hold or specify the pricing setting and conventions required. The proposed put-side equality should therefore be read as the question being investigated, not as a verified result. The document is useful as a prompt to examine option-price symmetry, but it offers little guidance for applying the identity without additional theory.

Key ideas

• The document asks whether a call-side symmetry identity has a corresponding put-side form.
• It expresses the proposed relationship using exchanged spot and strike arguments.
• The text provides no derivation or confirmation of the proposed equality.
• The assumptions and pricing conventions required for the symmetry are not specified.

Tags

# Put call symmetry of put


# Put call symmetry of put












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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