The identity
A European call and put with the same strike and expiry differ by a forward on the underlying. Intuitively: long call and short put deliver the same directional outcome as holding a forward that settles at that strike’s economics. Rearranged, it prices a put from a call (or vice versa) plus the forward.
Textbooks use rates and dividends. Crypto uses funding, basis, and whatever the settlement index is.
How to look at it on a chain
Pick one expiry and strike on /t/{asset}/chain. Compare call mark minus put mark to the distance between forward/index and strike, in the same unit. Wide markets will fake an edge. Inverse versus linear will fake an edge.
If calls and puts disagree violently, you probably mixed products or stale marks (partial feed), not discovered free money.
What people try to trade
Conversions/reversals and box-like packages when all legs are listed and margin is kind. On crypto, the competing instrument is often the perp. If perp funding plus basis is the real dislocation, you may not need options at all — see cash-and-carry.
Cross-venue parity trades inherit withdrawals, KYC, and two margin systems. Read arb-guide.
American-style and early exercise
Parity is cleaner for European cash-settled options — the usual crypto listed case. American early exercise (more of an equity story) breaks the simple identity. Always verify style on the venue spec.
European vs American guide is the companion.
Skew does not violate parity
Puts can be “expensive” versus calls in implied vol while parity still holds in price space. Skew lives in vol; parity lives in prices of matched strikes. Mixing the two languages causes fake paradoxes.
Use /t/{asset}/skew for vol language and the chain for price language.
Practice this on OptionsMatch
Same-strike call and put on /t/btc/chain. Term/basis desks for the forward story. Education — not an arb instruction.
If marks disagree, check sources first.