Home › Academy › Option pricing and the Greeks

Professional · Lesson 1 of 6

Put-call parity and no-arbitrage

7 minute read · By Krishna Avadhani, Vestora Academy · Updated 18 October 2026

For European options on a non-dividend-paying share, a call minus a put with the same strike and expiry must equal the share price minus the present value of the strike: C - P = S - K e^(-rT). If it did not, traders could lock in risk-free profit (arbitrage), and their trades would push prices back.

Parity shows that a long call plus cash equals a long put plus the share (the protective put). It lets you build "synthetic" positions: long call + short put = synthetic long share.

No-arbitrage reasoning underlies all derivatives pricing: a derivative must cost the same as any portfolio that exactly replicates its payoff.

Formula

C - P = S - K x e^(-rT)
(with dividends: C - P = S x e^(-qT) - K x e^(-rT))

Key takeaways

  • C - P = S - PV(K) for European options.
  • Synthetic long share = long call + short put.
  • No-arbitrage is the foundation of derivatives pricing.

Check your understanding

1. S = $100, K = $100, PV(K) = $97, call = $8. Put price by parity?

  • $3
  • $5
  • $8
  • $11
Show the answer

$5. P = C - S + PV(K) = 8 - 100 + 97 = $5.

2. Long call + short put (same strike/expiry) replicates...

  • A long put
  • A long share (synthetic)
  • Cash
  • A short call
Show the answer

A long share (synthetic). Its payoff equals owning the share minus the strike.

Go deeper

Practise this in Vestora

Look up real shares, test ideas with paper trading, and track your progress through the course.

Open the app free

General education only, not financial advice. Examples are illustrations. Rules, tax settings and products change; check official sources.