Statement and logic of put-call parity

Question

What is put-call parity for European options, and why must it hold?

Short answer

$C-P=S-Ke^{-rT}$ for options with the same strike and expiry on a non-dividend stock. A long call plus a short put pays $S_T-K$ in every state, exactly like a forward bought at $K$ , which is worth $S-Ke^{-rT}$ today. Two portfolios with identical payoffs must cost the same or there is an arbitrage. With dividends, replace $S$ by $S$ minus the PV of dividends.

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.13, p.17; question and answer rewritten by SelfMadeQuant.com.

See the hint and the full worked solution in the question bank (free account).

Open the worked solution

Lessons behind this question

No-Arbitrage Bounds and Put-Call Parity

Start with a free lesson: Options is part of a free topic. Create a free account, no card needed, to read it in full with worked solutions.

Read it free