Question

Q5. Some investors sometimes directly use put-call parity to American options. Does it make sense? Please explain.

Answer 1

Since American style options allow early exercise, put-call parity will not hold for American options unless they are held to expiration. Early exercise will result in a departure in the present values of the two portfolios.

In general, the relation does not hold for American-style options. It is so because American options allow early exercise prior to expiration. The put-call parity is a closed-end concept in which you define your starting point and know the outcome at the end.

Put-call parity applies only to European options, which can only be exercised on the expiration date, and not American options, which can be exercised before.

Put-call parity is an important concept in options pricing which shows how the prices of puts, calls, and the underlying asset must be consistent with one another. This equation establishes a relationship between the price of a call and put option which have the same underlying asset. For this relationship to work, the call and put option must have an identical expiration date and strike price.

The put-call parity relationship shows that a portfolio consisting of a long call option and a short put option should be equal to a forward contract with the same underlying asset, expiration, and strike price. This equation can be rearranged to show several alternative ways of viewing this relationship.

The put-call parity theory is important to understand because this relationship must hold in theory. With European put and calls, if this relationship does not hold, then that leaves an opportunity for arbitrage. Rearranging this formula, we can solve for any of the components of the equation. This allows us to create a synthetic call or put option. If a portfolio of the synthetic option costs less than the actual option, based on put-call parity, a trader could employ an arbitrage strategy to profit.