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Q: Put Call Parity Question ( No Answer,   3 Comments ) Question
 Subject: Put Call Parity Question Category: Business and Money Asked by: waynicemoves-ga List Price: \$5.00 Posted: 06 Nov 2006 18:08 PST Expires: 06 Dec 2006 18:08 PST Question ID: 780666
 ```Use put-call parity to prove that if a call and a put on the same stock and having the same expiration date are at-the-money, the call must be worth more than the put as long as there is time left before expiration. Can you provide an intuitive explanation for this result that does not refer to your proof? That is, why is it true that a call is worth more than its twin put if both are at the money?``` There is no answer at this time. ```Because a the execution of a put requires you to purchase and sell (transaction costs) the underlying value. A call involves just a single purchase.```
 ```Execution - Um no. The price of the call is higher because there is an expected return for the stock and that expected return is positive. As the stock price is expected to rise over time the options must be priced to include that rise. Note that dividends may disrupt this pricing relationship.```
 ```The equation for Put Call Parity is C + PV(X) = P + S where C = the current market value of the call; PV(x) = the present value of the strike price x, discounted from the expiration date at a suitable risk free rate; P = the current market value of the put; S= the current market value of the share It is derived purely using arbitrage arguments. It applies only to European options, since a possibility of early exercise could cause a divergence in the present values of the two portfolios. With regard to your example at the money means X=S Thus C=PV(S) = P+S As PV(S)P. This of course only hold if there are time to expiration left, otherwise S=PV(S) and C-P =0 and in this case C=P, which if at the money will mean C=P=0. But this is a special rare case. Intuitively this hold as well ? keep in mind the value of an option is linked to the probability or chance that it will end in the money and by how much this value is (X-S for a put and S-X for a call). For a put this value can be max X, thus if share falls to \$0, unlikely but then we did have a dot com boom! On the call side the value is maximum ? S-X but the share p[rice can go in theory to infinity. For example warren Buffets Berkshire Hathaway was listed I think for \$18 some 35y ago. But now is worth some \$90?000. Thus a 35y call strike \$18 would now be worth (\$90 000 -\$18) = \$89?982. While if it totally blew up and went bust to zero the put will only be worth \$18-0 = \$18. The chance that the call gives you to make insane amounts of money while the profit of a put is capped, implies that a call must be worth more than a put everything else being equal.``` 