Put-call parity calculator
A European call and put on the same stock with the same strike and expiry are tied together: their price difference must equal the stock price minus the present value of the strike. Choose what to find, enter the stock price, strike, interest rate, days to expiration and dividend yield, then the known option price. In check mode, enter both quotes to see whether one is rich against the other.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose to find the call price, the put price or to check both quotes.
- Enter the stock price, the strike, the risk-free rate and the days to expiration.
- Add a dividend yield if the stock pays dividends.
- Enter the known option price, or both prices in check mode.
C − P = S e^(−qT) − K e^(−rT), with T = days ÷ 365 and rates as yearly continuous rates.
- Call = P + S e^(−qT) − K e^(−rT)
- Put = C − S e^(−qT) + K e^(−rT)
- Gap = (C − P) − (S e^(−qT) − K e^(−rT))
Worked example
Stock 100, strike 100, rate 5 %, 365 days, no dividend:
- Present value of the strike = 100 × e^(−0.05) = 95.1229.
- With the put at 5.57, the call = 5.57 + 100 − 95.1229 = 10.4471.
- In check mode with quotes of 10.45 and 5.57, the gap is 0.0029: in line with parity.
With a stock at 50, strike 55, rate 4 %, dividend yield 2 %, 180 days and a call at 2, the put = 2 − 49.5093 + 53.9257 = 6.4164.
Tips
- Use the call and put with exactly the same strike and expiry.
- Use mid prices between bid and ask; parity with last trades can show gaps that are not there.
- For a quoted simple rate, the continuous rate is ln(1 + rate); at low rates the difference is small.
Frequently asked questions
What is the put-call parity formula?
C − P = S − K e^(−rT) for a stock without dividends, where T is in years and the rate is compounded continuously. With a dividend yield q, the stock term becomes S e^(−qT).
How do I get a call price from a put?
Call = put + S − K e^(−rT). With the stock and strike at 100, a 5 % rate and one year: the strike is worth 100 e^(−0.05) = 95.1229 today, so a put at 5.57 implies a call of 5.57 + 100 − 95.1229 = 10.4471.
Does it work for American options?
Not exactly. An American option can be exercised early, so parity becomes a range rather than an equation. For American calls on stocks without dividends it holds closely, because early exercise of such a call does not pay.
What does a gap mean?
If the call costs more than parity allows, a trader could sell the call, buy the put and the stock and borrow the present value of the strike, locking in the gap. In practice commissions, spreads and borrowing costs eat small gaps, so the calculator counts half a cent as in line.