Finance

Put-call parity is a relationship, first identified by Stoll (1969), that must exist between the prices of European put and call options that both have the same underlier, strike price and expirationdate. The relationship is derived using arbitrage arguments. Consider two portfolios consisting of:
[pic]The call option and an amount of cash equal to the present value of the strike price.[pic]The put option and the underlier.
Exhibit 1 compares the expiration value for these two portfolios, with x representing the common strike price: 

|Put-Call Parity:|
|Two Portfolios Have Identical Expiration Values |
|Exhibit 1|
|[pic] |
|[pic]|
|A portfolio comprising a call option and an amount x of cash equal to the present value of the |
|option's strike price hasthe same expiration value as a portfolio comprising the corresponding put |
|option and the underlier. For European options, early exercise is not possible. If the expiration |
|values of the twoportfolios are the same, then their present values must also be the same. This |
|equivalence is put-call parity. |


What issignificant about Exhibit 1 is the fact that the two portfolios (call + cash and put + underlier) have identical expiration values. Irrespective of the value of the underlier at expiration, eachportfolio will have the same value as the other.
If the two portfolios are going to have the same value at expiration, then they must have the same value today. Otherwise, an investor could make an...