Put–Call Parity, explained.
Put–call parity is a no-arbitrage relation between European put and call prices, the underlying asset and the present value of the strike under stated assumptions.
Why it happens
A call plus a bond paying strike one hundred matches a put plus a share at every selected terminal stock price. Market-quote presets either satisfy equality or overprice one option by three.
Put–call parity is a no-arbitrage relation between European put and call prices, the underlying asset and the present value of the strike under stated assumptions.
Read the result
Initial cost and terminal payoff belong to different dates. The two portfolios’ equal terminal payoffs persist across the selected stock-price scenarios.
A worked example
Check replication before discussing market direction
Keep matched quotes and compare call-plus-bond cost with put-plus-share cost.
Move terminal stock price below and above strike one hundred, checking equal payoffs in both regions.
Choose the overpriced-call preset and observe initial cost differ by three while terminal payoff difference remains zero.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A call plus a bond paying strike one hundred matches a put plus a share at every selected terminal stock price. Market-quote presets either satisfy equality or overprice one option by three.
Where this idea is useful
A practical use
Use payoff replication to distinguish an inconsistent price relationship from a forecast about the underlying asset.
A common misconception
“An option price inconsistency is simply a forecast that the stock will rise.”
Put–call parity compares replicating payoffs under no-arbitrage assumptions. It does not require a directional prediction about the stock.
What this explanation leaves out
- European exercise, no dividends, a five-percent risk-free rate and frictionless financing are assumed. Actual borrowing, spreads and contract features can prevent execution of an ideal arbitrage.
Can I execute the displayed difference as a real trade?
The benchmark omits spreads, borrowing restrictions, exercise features and dividends, so a model mismatch alone is not an execution plan.
Do the portfolios match in every relevant terminal state, not just the scenario you prefer?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.