Synthetic Forward (Put-Call Parity)
Computes the synthetic forward price implied by the prices of a European call and put with the same strike and expiry, via put-call parity: F = (C − P)·e^(rT) + K. Instead of starting from the spot price and cost of carry, it extracts the forward directly from the options market, which is useful for checking arbitrage between the two markets. Enter the call and put premiums, the strike, the interest rate and the term.
Result
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Synthetic Forward (Put-Call Parity)
Computes the synthetic forward price implied by the prices of a European call and put with the same strike and expiry, via put-call parity: F = (C − P)·e^(rT) + K. Instead of starting from the spot price and cost of carry, it extracts the forward directly from the options market, which is useful for checking arbitrage between the two markets. Enter the call and put premiums, the strike, the interest rate and the term.
The forward hidden inside the options
There's a rigid relationship between a call's price, a put's price at the same strike and the asset's forward price. It's put-call parity, and it allows an elegant trick: extracting the implied forward without looking at the spot price, using only the option premiums. If the call is worth more than the put, the market is saying the forward is above the strike, and the formula quantifies by how much.
The expression is F = (C − P)·e^(rT) + K. The practical appeal is the arbitrage check: if the forward implied by the options differs from the forward traded in the futures market, there's an inconsistency to exploit. That's why derivatives traders compute this number constantly, cross-referencing the two markets in search of mismatches.
Enter the call and put premiums, the strike, the continuous interest rate and the term. The tool returns the synthetic forward. Keep in mind exact parity only holds for European options; in American options, the early-exercise premium breaks the equality and the number becomes just an approximation.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.