Put-call parity: conversion, reversal and why the forward matters
A call minus a put with the same strike behaves like the underlying minus the strike. If the link breaks, it can be locked in with three trades on one exchange. We check parity on live prices and see why a 0.34% “deviation” is usually basis, not free money.
Cross-exchange setups (lesson 5) keep the legs on different exchanges. Put-call parity lets you look for dislocations inside one exchange: a call, a put and the underlying with the same strike and expiry are linked by a formula, and if it breaks, the gap can be locked in.
The formula
For European options with the same strike and expiry: call − put = (forward − strike) × discount. The meaning is simple: a bought call plus a sold put together behave like buying the underlying at the strike price on the expiry date — a synthetic future. If the call and put are priced differently from the real future, one of the combinations is cheaper.
For Deribit coin options, where the premium and payoff are in BTC, the same logic gives: call − put (in BTC) ≈ 1 − strike ÷ forward.
Conversion and reversal
- Conversion (the call is rich): sell the call, buy the put, buy the underlying. By expiry the position locks in the gap.
- Reversal (the call is cheap): buy the call, sell the put, sell the underlying.
- All three legs are on one exchange — margin is calculated together, with no liquidation risk on another venue.
Checking it on live prices
| Exchange | Call − put (mid prices) | Using the forward | Using spot |
|---|---|---|---|
| Deribit, in BTC | −0.0265 BTC | 1 − 80,000 ÷ 77,938.75 = −0.0264 | 1 − 80,000 ÷ 77,285.35 = −0.0351 |
| Bybit, in USDT | −$1,922.5 | 78,053.86 − 80,000 = −$1,946.1 | 77,285.35 − 80,000 = −$2,714.6 |
- With the forward parity holds almost exactly: on Deribit the difference is 0.00005 BTC (about $4), on Bybit $24. That is less than the bid/ask spread — there is nothing to earn.
- With spot the “deviation” is huge: about $667 on Deribit and $792 on Bybit, or 1.02% of the BTC price. That is not a market error but the basis: the 55-day forward is pricier than spot.
What the scanner shows
The scanner calculates parity from the index (spot) — its risk note says so plainly: for longer maturities carry appears as deviation and is not free profit. In the screenshot the deviation is $291.68 (+0.34%) over 23.4 days — about 5.3% a year. The annualized basis of the BTC quarterly future on Binance that day was 5.13%. The conversion here is the same cash-and-carry trade (futures course), just built from options: the +0.22% over 23 days after fees roughly equals what the basis pays.
When parity is a real opportunity
- One strike shows a deviation while its neighbors do not — the issue is that specific option, not carry.
- The deviation is noticeably larger than the futures basis for the same date.
- All three legs are executable at bid and ask, not just mid prices, and the fees for three legs are covered. Deribit offers a combo discount: the fees of the legs in one direction are reduced to zero.
- A study of parity on Binance ETH options (Finance Research Letters, 2024) found that significant violations remain even after spreads and fees — but they have to be caught quickly and execution has to be checked.
Frequently asked questions
What is put-call parity?
The link between the prices of a European call and put with the same strike and expiry and the underlying: call − put = (forward − strike) × discount. A bought call plus a sold put together behave like a future at the strike price.
How is conversion different from reversal?
Conversion: sell the call, buy the put and buy the underlying when the call is rich. Reversal: buy the call, sell the put and sell the underlying when the call is cheap.
Why compare parity with the forward rather than spot?
Options settle on the expiry date, and the forward for that date is pricier than spot by the basis. Plug in spot and the basis looks like a “deviation”, even though it is ordinary carry.
Is the scanner’s parity deviation a profit?
Not necessarily. The scanner calculates from spot, so for longer maturities the deviation includes the basis. A real opportunity is when an individual strike shows a deviation noticeably larger than the futures basis.
Sources
- 1.Put/Call ParityOptions Industry Councilofficial
- 2.Deribit Position Builder: primer on basic option strategiesDeribit Insights1/20/2021
- 3.
- 4.Put–call parity in a crypto option market — Evidence from BinanceFelföldi-Szűcs, Králik, Váradi1/1/2024
- 5.FeesDeribit10/22/2026
- 6.P2P.Army: cash-and-carry — the spot–futures basisP2P.Army10/31/2026
- 7.P2P.Army: options arbitrage scannerP2P.Army10/31/2026
About the author
Crypto expert, arbitrage trader and investor
Crypto expert and hands-on crypto arbitrage trader, investor and software developer with over 20 years of experience. On the P2P.Army blog he covers exchange news, P2P and cross-exchange arbitrage.
- Crypto arbitrage
- P2P arbitrage
- Cross-exchange arbitrage
- Crypto exchanges
- Investing
- Software development
