Finance & Options
Put-Call Parity for Dummies
Two portfolios with the same payoff must cost the same, and that one rule gives put-call parity, C − P = S − K e^(−rT), with no model at all.
What to remember
- An arbitrage costs nothing, never loses, and sometimes pays; no-arbitrage pricing asks what prices must be for none to exist.
- Call plus a bond paying K and put plus a share both pay max(S_T, K), so C + K e^(−rT) = P + S.
- To trade a parity violation, buy the cheap side, sell the rich side, and hedge with the stock and a bond; the discount rate decides which side is cheap.
- max(S − K e^(−rT), 0) ≤ C ≤ S, so an American call on a non-dividend stock is never exercised early.
- A butterfly (buy calls at K₁ and K₃, sell two at the midpoint K₂) never pays less than zero, so C(K₂) ≤ (C(K₁) + C(K₃))/2: call prices are convex in the strike.
- Call and put struck at the forward F = S e^(rT) cost the same; with dividends of present value D, parity becomes C − P = S − D − K e^(−rT).
Read the lessonNo-Arbitrage and Put-Call Parity, with a checkpoint at the end.