Put-Call Parity Calculator
Check put–call parity for European options — compare C − P against S − K·e^(−rT) to spot an arbitrage gap between a call, a put, the stock and cash.
How it works
Put–call parity: C − P = S − K·e^(−rT) · Arbitrage gap = (C − P) − (S − K·e^(−rT))
Put–call parity ties together a European call, a European put at the same strike and expiry, the underlying and a bond. If the equality breaks, a risk-free arbitrage exists: hold the cheap side and short the expensive side to lock in the gap. In liquid markets the relationship holds tightly, so a large gap usually signals a data error, a dividend, or borrow costs rather than free money.
Worked example
With a $8 call, a $6 put, a $100 stock, a $100 strike, a 4% rate and half a year: C − P = $2, while S − K·e^(−0.02) = 100 − 98.02 = $1.98. The gap is just $0.02 per share, so parity effectively holds.
Sources: Put–call parity (Wikipedia)
Frequently asked questions
What breaks put–call parity in practice?
Dividends, hard-to-borrow stock, early-exercise features of American options, and transaction costs. Each adds a term or a friction that shifts the equality; a raw gap often reflects one of these rather than true arbitrage.
Does parity work for American options?
Not as an exact equality. American options can be exercised early, which adds value that the simple formula ignores. Parity becomes a pair of inequalities rather than a single equation.
How do I exploit a real gap?
A conversion — long stock, long put, short call at the same strike — locks in the difference if the call is rich. A reverse conversion does the opposite. After costs and borrow, genuine edges are tiny and fleeting.
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Educational estimate using a simplified Black–Scholes / options model — no dividends, no early-exercise, no fees or slippage. Options are high-risk. Not investment advice.