to buy the stock at the same strike price. It doesn’t matter what the strike
price is. As long as the strike is the same for the call and the put, the trader
will have a long position in the underlying at the shared strike at expiration
when exercise or assignment occurs.
The options in this example are 50-strike options. At expiration, the trader
can exercise the call to buy the underlying at $50 if the stock is above the
strike. If the underlying is below the strike at expiration, he’ll get assigned
on the put and buy the stock at $50. If the stock is bought, whether by
exercise or assignment, the effective price of the potential stock purchase,
however, is not necessarily $50.
For example, if the trader bought one 50-strike call at 3.50 and sold one
50-strike put at 1.50, he will effectively purchase the underlying at $52
upon exercise or assignment. Why? The trader paid a net of $2 to get a long
position in the stock synthetically (3.50 of call premium debited minus 1.50
of put premium credited). Whether the call or the put is ITM, the effective
purchase price of the stock will always be the strike price plus or minus the
cost of establishing the synthetic, in this case, $52.
The question that begs to be asked is: would the trader rather buy the
stock or pay $2 to have the same market exposure as long stock?
Arbitrageurs in the market (with the help of the put-call parity) ensure that
neither position—long stock or synthetic long stock—is better than the
other.
For example, assume a stock is trading at $51.54. With 71 days until
expiration, 26.35 IV, a 5 percent interest rate, and no dividends, the 50-
strike call is theoretically worth 3.50, and the 50-strike put is theoretically
worth 1.50. Exhibit 6.7 charts the synthetic stock versus the actual stock
when there are 71 days until expiration.