Put-Call Parity and Forward Parity

Put-Call Parity

• Put-call parity defines a relationship that links the price of a call option to the price of a put option, and vice versa, provided they share the same underlying details (asset, strike price, expiration date).

• This parity is valid for European options possessing identical exercise prices and expiration dates.

• It signifies a no-arbitrage condition between the prices of:

  • Put option
  • Call option
  • Underlying asset
  • Risk-free asset

• If the put-call parity is violated, arbitrage opportunities may arise, enabling investors to generate riskless profits.

Put-Call Forward Parity

• Put-call forward parity broadens the put-call parity concept to forward contracts.

• It is based on the principle that holding an underlying asset is equivalent to holding a long forward contract combined with a risk-free bond.

• Under put-call forward parity:

  • Buying a put option and selling a call option equals holding a long risk-free bond and a short forward position.
  • Selling a put option and buying a call option equals holding a long forward position and a short risk-free bond.

Applications Beyond Options

• Put-call parity isn't confined to option-based strategies; its applications extend to broader finance concepts.

  • For instance, equity holders can be viewed as holding a bought call option on the firm's value, with unlimited upside potential.
  • Conversely, debtholders are akin to holding a sold put option on the firm's value, with limited upside.