How this number is made
Put-call parity says a European call minus a European put equals the share, after dividends, minus the strike discounted at interest. If the premiums you type do not match that, the difference is the gap. Borrow constraints, early exercise, and a wide bid-ask can keep the gap from being a free trade.
- Premiums are per share.
- The rate and the dividend yield are annual, and the years match the expiration.
Formula
Fair call − put = Se^(−qT) − Ke^(−rT). Gap = (market call − market put) − that value.
Worked example
With the figures already in the form, gap, market minus fair is $0.00.
Questions
Does this work for American options?
Only as an approximation. An American put can be exercised early, so the European identity is not exact.
Is a gap a profit?
Only if you can trade all four pieces, including the stock borrow or the financing, inside the gap. This page does not price those frictions.