Put-call parity

A call plus cash and a put plus the share are worth the same at expiry whatever happens, so they must cost the same today. Arithmetic enforced by arbitrage, not a model.

Where you will meet it

Put-call parity appears in 4 learning outcomes on the CFA syllabus. A few of them:

• Use put-call parity to link option prices with the underlying's price
  CFA Level I · Derivatives

  “Put-call parity says that a put plus the underlying equals a call plus the present value of the exercise price: p + S = c + X/(1+r)^T.”

• Explain how the Black model values European options on futures contracts
  CFA Level II · Derivatives and Risk Management

  “Both F and X are discounted, so put–call parity for options on futures becomes c = p + e^(−rT)(F − X).”

• Show how a combination of options can reproduce the return profile of an underlying asset
  CFA Level III · Derivatives and Risk Management

  “Replication rests on put–call parity for an asset that pays no income: S + p = c + PV(X).”

• Say what implied volatility is and how options traders use it
  CFA Level II · Derivatives and Risk Management

  “Put–call parity implies a European call and put with the same strike and expiry should carry the same implied volatility.”

See also

Arbitrage

Practise it

• Today's practice question One question, with every wrong option explained.
• Free Level I diagnostic test Twelve questions that show which topics to start with.
• Free finance calculators Check your arithmetic on the exam's core formulas.

All terms beginning with P · Glossary