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Options & Put-Call Parity (Page 2 of 2)
Date Added: June 9th, 2004

By Dan Schuster | E-mail

             P + S = C + E * [1/(1+i)] ^n     where:
 
   P = the market price of the put
   S = the market price of the stock
   C = the market price of the call
   E = the exercise price of both the call and the put
   i = the risk free rate
   n = the number of years until the expiration date of the options

   Because the algebraic derivation of this equation is rather complex and somewhat lengthy, it will be much easier to prove it graphically and discuss the formula and its application. 

   The graph on the left is simply the graph from the hedging section except it uses the value of the call rather than the gain.  The graph on the right is common sense because the present value of the cash is unaffected by the value of the stock.  Finally, the graph below is a combination of the other two.

   Again, the graph on the left is simply the graph from the hedging section except it uses the value of the put rather than the gain.  The graph on the right is common sense because it has the value of the stock on both axes.  Finally, the graph below is a combination of the other two.

                               

   Now that we see why put-call parity works, it is simple to apply it.  At any point in time, there are only really 2 variables an investor seeking to use options for speculative purposes needs to look at:  P and C.  You take all the other ones as given.  Thus, if P + S > C + E * [1/(1+i)] ^n, you should buy calls because their value must increase for the equation to balance.  On the other hand if P + S < C + E * [1/(1+i)] ^n, you should buy puts.

   To summarize everything, using options to hedge can help protect your investments.  And using options to speculate can earn you high returns.  But it's important to remember that options take a lot of work to master.

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