Put–Call Parity and Different Implied Volatilities

Summary

The document asks how vanilla put–call parity relates to the possibility that puts and calls on the same underlying appear to have different implied volatilities. It names short-sale restrictions, borrowing costs, and an underlying that is not traded as potential reasons for differences. The author proposes that parity may align the implied volatility of a long call with a short put, and of a short call with a long put, while allowing same-direction option positions to differ.

This is a conceptual question rather than a demonstrated result: it provides no market example, pricing derivation, or answer. Its useful focus is the distinction between parity relationships for combined option positions and observed implied volatilities, which depend on pricing inputs and trading frictions. The stated parity relation is simplified in the document, and the discussion does not specify carry, dividends, financing, or the precise meaning of its forward-price notation. Those omissions limit what can be concluded from the proposed interpretation.

Key ideas

• The document considers put–call parity alongside observed differences in put and call implied volatilities.
• It identifies shorting constraints, borrowing costs, and an untraded underlying as possible sources of pricing differences.
• It proposes that parity may link implied volatilities for certain opposite-direction call and put positions.
• The question gives no derivation or answer and leaves financing and carry assumptions unspecified.

Tags

# Put-call parity and different IVs for puts and calls


# Put-call parity and different IVs for puts and calls












For vanilla options put-call parity $$ C - P = F $$ must hold. On the other hand, it can happen that puts can have different implied vols than calls, due to for example shorting restrictions, borrowing costs, or if the underlying is not traded.

My interpretation would be that a long call and short put must have the same IV, and a short call and long put must have the same IV as well, but not necessarily a long call and long put, or short call and short put.

Does this make sense? Am I overlooking something?

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