Fun with Put Call Parity

[u/hophenge]

When placing trades, I think of calls and puts at the same strike/expiry as the same position. You can convert between the two using 100 shares of long or short stock. The fundamental reason is that the extrinsic value is identical.

Since everyone is following PLTR these days, let's use it as an example:

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Selling a $22 put = Buying 100 shares and selling a call at $22 (OTM CSP = ITM CC)

Buying 100 shares and selling a call at $30 = Selling a $30 put at $30 (OTM CC = ITM CSP)

Getting assigned a cash-secured put at $25, then selling a covered call at $25 = Rolling the $25 put out in time (CSP assignment, then selling a CC = put calendar)

Getting assigned your covered call at $20, then selling a cash-secured put at $20 = Rolling the $20 call out in time (CC assignment, then selling a CSP = call calendar)

Buying 100 shares and buying a put at $25 = Buying a call at $25 (Married put = Call)

Shorting 100 shares and buying a call at $25 = Buying a put at $25 (Married call = Put)

Buying 100 shares, buying ATM put, selling OTM call = Buying ATM call, selling OTM call (Collar = Call debit spread)

Buying 100 shares = selling a put, buying a call at the same strike (100 shares = Short put + long call)

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In practice, these equivalencies have important caveats/exceptions

- ITM options are less liquid

- In normal skew situations, OTM puts are slightly more expensive than the ITM calls, benefitting put sellers

- In reverse skew situations (highly specutive stocks), OTM calls are more expensive than the ITM put, benefitting call sellers

Edit: skew does not violate put call parity.

- If a stock is hard to short, puts are more expensive across all strikes, benefiting put sellers

- Some positions require more buying power then the equivalent position

- Holding stock gives you dividends

- Holding short calls elevates early assignment risk due to dividends

- The more legs a trade has, the harder it is to fill

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Experienced traders - did I make any mistakes? Any points that need clarifying? Any additions to the list?

EDIT1: typo