Put-Call Parity Calculator: Determine Future Price in Options Trading
Put-call parity lets you estimate the underlying’s forward price by combining one call, one put and cash. Enter call, put and strike; the tool applies S = C − P + K. Example: an $8.40 call, $3.10 put and $105 strike imply $110.30. About 76 % of listed options expire worthless (CBOE, 2023), so parity helps you avoid mispriced contracts.
Put-Call Parity Calculator
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How to use the tool
1. Call Price (C) – type any non-negative value, e.g., $8.40 or $12.25.
2. Put Price (P) – enter a matching-maturity put, e.g., $3.10 or $1.95.
3. Strike Price (K) – supply the shared exercise price, e.g., $105.00 or $130.00.
4. Calculate – the form returns the implied future price S.
Formula
For European options without dividends and with a short maturity, the present value of the strike approximates K, giving:
$$S = C – P + K$$
Full expression:
$$C + PV(K) = P + S$$
Example 1
C = $8.40
P = $3.10
K = $105.00
Implied S = 8.40 − 3.10 + 105.00 = $110.30
Example 2
C = $12.25
P = $1.95
K = $130.00
Implied S = 12.25 − 1.95 + 130.00 = $140.30
Quick-Facts
Works for European options only; early exercise skews parity (Hull, 2022).
Inputs must be non-negative real numbers (SEC, https://www.sec.gov).
Assumes flat interest; adjust PV(K) with r ≈ 4 % for one-year terms (FRED, 2023).
Typical retail option commission: $0.65 per contract (Schwab, 2023).
FAQ
What does the calculator deliver?
It outputs the implied future spot price of the underlying, calculated with S = C − P + K (Investopedia, https://tinyurl.com/putcallparity).
Which option style fits put-call parity?
Parity holds exactly for European options that can be exercised only at expiry (Hull, 2022).
How can I detect arbitrage?
Compare S from the tool with today’s spot; gaps beyond transaction costs signal arbitrage (CBOE, 2023).
Dividend payments lower call value and raise put value; adjust S by subtracting PV(dividends) (Black & Scholes, 1973).
Why can S differ from current price?
Premiums price in expected volatility and cost of carry, moving S above or below spot (Natenberg, 2015).
Can I apply this to commodities?
Yes, as long as the options are European and share strike and expiry (CME Group, 2023).
What if my inputs turn negative?
The form rejects negatives; option prices cannot be below zero in regulated markets (SEC, https://www.sec.gov).
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