Synthetic Long Call—Mechanics at Expiration

Consideration of what happens with the stock price above, below, or at the strike price at expiration leads to the conclusion that the synthetic long call results in the same position, with the same profit or loss, and with the same effective price as if a real 100 Call had been purchased for 3.00.When the stock price closes above $100 at expiration, the long 100 Put is out of the money and expires worthless, but the long stock position remains intact.

The effective price of the long stock position in this example is $103, which is calculated by adding the 3.00 cost of the put to the purchase price of the stock of $100. Thus, with the stock price above the strike price at expiration, the synthetic long call position described in Table 5-3 and Figure 5-3 becomes a real long stock position at an effective price of $103—the same result as buying a real 100 Call for 3.00 and exercising it.If the stock price falls below $100 at expiration, then the long 100 Put is in the money and is exercised.

Exercise of a long put creates a stock sale transaction, which means that the stock is sold at $100. The result is a loss of 3.00 per share (from the cost of the put) and no position other than the $100 cash reserve. Thus, with the stock price below the strike price at expiration, the synthetic long call position described in Table 5-3 and Figure 5-3 becomes a cash position with a loss equal to 3.00.

This result is the same as buying a 100 Call for 3.00 and holding a $100 cash reserve;In the third outcome, the stock price closes exactly at $100 at expiration,the long 100 Put expires worthless, and the long stock position remains intact. However, if the stock were sold at $100 after the put expires, then the result would be a loss of the cost of the put of 3.00 and no position other than the $100 cash reserve. This result is the same as buying a 100 Call at 3.00 and holding a cash reserve of $100; at expiration, the call expires worthless, and the cash reserve remains intact.

The conclusion is that the two-part position of long stock and a long put behaves exactly the same as a real long call position. It therefore deserves its name, synthetic long call.Synthetic Short Call:A synthetic short call is created with short stock and a short put.Table 5-4 and Figure 5-4 illustrate that short stock at $100 and a short 100 Put at 3.00 are equivalent to a short 100 Call at 3.00. Table 5-4 shows the profit-and-loss calculations for each component of the synthetic position, for the combined position, and for the corresponding real position at various stock prices.

Figure 5-4 graphs the components and the combined position.Row 2 in Table 5-4 assumes a stock price of $95 at expiration (column1). The stock sold short at $100 makes a profit of 5.00 per share (column 2), and the 100 Put sold at 3.00 suffers a loss of 2.00 per share (column 3). Subtracting the put loss from the stock profit yields a net profit of 3.00 per share (column 4). A 100 Call sold at 3.00 (column 5) would generate the same profit per share.

Any row in Table 5-4 proves that the combination of the short stock and short put listed in column 4 produces the same result as selling a 100 Call at 3.00 in column 5.Synthetic Short Call—Mechanics at Expiration:A consideration of what happens with the stock price above, below, or at the strike price at expiration leads to the conclusion that the synthetic short call results in the same position, with the same profit or loss, as if a real 100 Call had been sold at 3.00.

If the stock price is above $100 at expiration, then the short 100 Put lands out of the money and expires worthless, whereas the short stock position remains intact. The effective sale price of the short stock position in this example is $103 because the put premium received of 3.00 is added to the sale price of the stock of $100. Thus, with the stock price above the strike price at expiration, the synthetic short call position described in Table 5-4 and Figure 5-4

becomes a short stock position,just as a real short call would be assigned and become a short stock position.When the stock price falls below $100 at expiration, then the short 100 Put is in the money and is assigned. Assignment of a short put creates a stock purchase transaction, meaning that the short stock position is covered. The result is a profit of 3.00 and no position other than the cash reserve of $100. Thus, with the stock price below the strike price at expiration, the synthetic short call position described in Table 5-4 and Figure 5-4 becomes a cash position with a profit equal to 3.00.