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 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.

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.