the 100 Put purchased for 3.00 makes 2.00 per share(column 3). Adding the two proﬁts yields a total proﬁt of 5.00 pershare (column 4), the same proﬁt per share of 5.00 that is earnedon stock sold short at $100 per share (column 5). In any row inTable 5-2, the combination of the short call and long put in column4 reaches the same result as selling stock short at $100 per share incolumn 5.
Synthetic Relationships • 141
Synthetic Short Stock—Mechanics at ExpirationComparing the results of the positions when the stock price closesabove, below, or at the strike price at expiration leads to the conclusion that the synthetic short stock position results in the same position,with the same proﬁt or loss, and with the same effective price as if realstock has been sold short at $100 per share.With a stock price above $100 at expiration, the long 100 Put is outof the money and expires worthless. The short 100 Call, however,closes in the money and is assigned. Assignment of a short call createsa stock sale transaction. It is assumed that the $100 cash reserve is usedas margin to support the resulting short stock position.If the stock price falls below $100 at expiration, then the short 100Call is out of the money and expires worthless, but the long 100 Putis in the money and is exercised. Exercise of a put creates a stock saletransaction, which creates a short stock position at an effective priceof $100. As above, the $100 cash reserve is used as margin.If the stock price closes exactly at $100 at expiration, then both the100 Call and the 100 Put expire worthless, resulting is no position andno proﬁt or loss. However, stock could be sold short at $100 after bothoptions expire worthless, and the result would be a short stock position with no proﬁt or loss—the same result as shorting real stock originally at $100 per share.The conclusion is that a two-part position of a short call and a longput behaves exactly the same as a real short stock position. It thereforedeserves its name, synthetic short stock.
Synthetic Long CallA synthetic long call consists of long stock and long puts on a sharefor-share basis. Table 5-3 and Figure 5-3 illustrate that long stock at100 and a long 100 Put at 3.00 are equivalent to a long 100 Call at3.00. Table 5-3 shows the proﬁt-and-loss calculations for each component of the synthetic position, for the combined position, and forthe corresponding real position at various stock prices. Figure 5-3graphs the components and the combined position.
142 • Trading Options As a Professional
Table 5-3
Synthetic Long Call: Long Stock at 100 and Long 100 Put at 3.00Compared with Long 100 Call at 3.00Col 1
Col 2
Col 3
Col 4
Col 5
Long 100Put @ 3.00
CombinedP/(L)
Long 100Call @ 3.00
10.005.00-05.0010.00
7.002.003.003.003.00
3.003.003.002.007.00
3.003.003.002.007.00
95
100
Stock Price Long Stockat Expiration@ 100Row 1Row 2Row 3Row 4Row 5
9095100105110
10
P/(L)
50–5–10
Long Stock @ 100Figure 5-3
Stock PriceLong100 Put @ 3
105Long100 Call @ 3
Synthetic Long Call = Long Stock and Long Put
Row 4 in Table 5-3 assumes a stock price of $105 at expiration (column 1). The stock purchased for $100 per share makes a proﬁt of 5.00(column 2), and the 100 Put purchased for 3.00 suffers a loss of 3.00(column 3). Subtracting the put loss from the stock proﬁt yields a netproﬁt of 2.00 (column 4), the same proﬁt per share of 2.00 that isearned on a 100 Call purchased for 3.00 per share (column 5). Anyrow in Table 5-3 proves that the combination of the long stock andlong put in column 4 reaches the same result as purchasing a 100 Callat 3.00 in column 5.
Synthetic Relationships • 143
Synthetic Long Call—Mechanics at ExpirationConsideration of what happens with the stock price above, below, orat the strike price at expiration leads to the conclusion that the synthetic long call results in the same position, with the same proﬁt orloss, and with the same effective price as if a real 100 Call had beenpurchased for 3.00.When the stock price closes above $100 at expiration, the long 100Put is out of the money and expires worthless, but the long stock position remains intact. The effective price of the long stock position inthis example is $103, which is calculated by adding the 3.00 cost ofthe put to the purchase price of the stock of $100. Thus, with the stockprice above the strike price at expiration, the synthetic long call position described in Table 5-3 and Figure 5-3 becomes a real long stockposition at an effective price of $103—the same result as buying a real100 Call for 3.00 and exercising it.If the stock price falls below $100 at expiration, then the long 100Put is in the money and is exercised. Exercise of a long put creates astock sale transaction, which means that the stock is sold at $100. Theresult 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 belowthe strike price at expiration, the synthetic long call position describedin Table 5-3 and Figure 5-3 becomes a cash position with a loss equalto 3.00. This result is the same as buying a 100 Call for 3.00 and holding a $100 cash reserve; at expiration, the call expires, and the cashreserve remains intact.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 theput expires, then the result would be a loss of the cost of the put of3.00 and no position other than the $100 cash reserve. This result isthe 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 reserveremains intact.
144 • Trading Options As a Professional
The conclusion is that the two-part position of long stock and a longput behaves exactly the same as a real long call position. It thereforedeserves its name, synthetic long call.
Synthetic Short CallA 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 short100 Put at 3.00 are equivalent to a short 100 Call at 3.00. Table 5-4shows the proﬁt-and-loss calculations for each component of the synthetic position, for the combined position, and for the correspondingreal position at various stock prices. Figure 5-4 graphs the componentsand the combined position.Row 2 in Table 5-4 assumes a stock price of $95 at expiration (column 1). 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 pershare (column 3). Subtracting the put loss from the stock proﬁtyields a net proﬁt of 3.00 per share (column 4). A 100 Call sold at3.00 (column 5) would generate the same proﬁt per share. Any rowin Table 5-4 proves that the combination of the short stock and shortput listed in column 4 produces the same result as selling a 100 Callat 3.00 in column 5.Table 5-4
Synthetic Short Call: Short Stock at 100 and Short 100 Put at3.00 Compared with Short 100 Call at 3.00Col 1
Col 2
Stock Price Short Stockat Expiration@ 100Row 1Row 2Row 3Row 4Row 5
9095100105110
10.005.00-05.0010.00
Col 3
Col 4
Col 5
Short 100Put @ 3.00
CombinedP/(L)
Short 100Call @ 100
7.002.003.003.003.00
3.003.003.002.007.00
3.003.003.002.007.00
Synthetic Relationships • 145
10
P/(L)
50–5–1095Short Stock @ 100
Figure 5-4
100Stock PriceShort 100 Put @ 3
105Short 100 Call @ 3
Synthetic Short Call = Short Stock and Short Put
Synthetic Short Call—Mechanics at ExpirationA consideration of what happens with the stock price above, below, orat the strike price at expiration leads to the conclusion that the synthetic short call results in the same position, with the same proﬁt orloss, 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 Putlands out of the money and expires worthless, whereas the short stockposition remains intact. The effective sale price of the short stock position in this example is $103 because the put premium received of 3.00is added to the sale price of the stock of $100. Thus, with the stockprice 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 shortstock position.When the stock price falls below $100 at expiration, then the short100 Put is in the money and is assigned. Assignment of a short put creates a stock purchase transaction, meaning that the short stock positionis covered. The result is a proﬁt of 3.00 and no position other than thecash reserve of $100. Thus, with the stock price below the strike price atexpiration, the synthetic short call position described in Table 5-4 andFigure 5-4 becomes a cash position with a proﬁt equal to 3.00. This result
146 • Trading Options As a Professional
is the same as selling a 100 Call for 3.00 and holding a $100 cash reserve;at expiration, the call expires, and the cash reserve remains intact.In the third outcome, the stock price closes exactly at $100 at expiration, the short 100 Put expires worthless, and the short stock position remains intact. However, if the short stock were covered after theput expires, then the result would be a proﬁt of 3.00 and no positionother than the $100 cash reserve. This result is the same as selling a100 Call at 3.00 and holding a cash reserve of $100; at expiration, thecall expires, and the cash reserve remains intact.The conclusion is that the two-part position of short stock and shortput behaves exactly the same as a real short call position. It thereforedeserves its name, synthetic short call.
Synthetic Long PutA synthetic long put is created with short stock and a long call on ashare-for-share basis. Table 5-5 and Figure 5-5 illustrate that short stockat 100 and a long 100 Call at 3.00 are equivalent to a long 100 Put at3.00. Table 5-5 shows the proﬁt-and-loss calculations for each component of the synthetic position, for the combined position, and forthe corresponding real position at various stock prices. Figure 5-5graphs the components and the combined position.Table 5–5
Synthetic Long Put: Short Stock at 100 and Long 100 Call at 3.00Compared with a Long 100 Put at 3.00Col 1
Col 2
Stock Price Short Stockat Expiration@ 100Row 1Row 2Row 3Row 4Row 5
9095100105110
10.005.00-05.0010.00
Col 3
Col 4
Long 100 CombinedCall @ 3.00P/(L)3.003.003.002.007.00
7.002.003.003.003.00
Col 5Long 100Put @ 3.007.002.003.003.003.00
Synthetic Relationships • 147
10
P/(L)
50–5–1095Short Stock @ 100Figure 5-5
100Stock PriceLong100 Call @ 3
105Long100 Put @ 3
Synthetic Long Put = Short Stock and Long Call
Row 2 in Table 5-5 assumes a stock price of $95 at expiration (column 1). The stock sold short at $100 makes a proﬁt of 5.00 per share(column 2), and the 100 Call purchased for 3.00 incurs a loss of 3.00per share (column 3). Subtracting the call loss from the stock proﬁtyields a net proﬁt of 2.00 per share (column 4). This proﬁt per shareof 2.00 is the same as would be earned had a 100 Put been purchasedfor 3.00 (column 5). In any row in Table 5-5, the combination of theshort stock and long call in column 4 reachs the same result as purchasing a 100 Put for 3.00 in column 5.
Synthetic Long Put—Mechanics at ExpirationConsidering what happens with the stock price above, below, or at thestrike price at expiration leads to the conclusion that the synthetic longput position results in the same position, with the same proﬁt or loss,as if a 100 Put had been purchased for 3.00 per share. If the stock priceis above $100 at expiration, then the long 100 Call is in the moneyand is exercised. Exercising a long call creates a stock purchase transaction, which covers the short stock. The effective price of purchasing stock in this example is $103 because the cost of the call of 3.00is added to the strike price of 100. Thus, with the stock price above
148 • Trading Options As a Professional
the strike price at expiration, the synthetic long put position describedin Table 5-5 and Figure 5-5 results in no stock position with a loss of3.00 per share, just as a real long 100 Put purchased for 3.00 wouldexpire worthless and leave no position except the cash reserve.When the stock price is below $100 at expiration, then the long 100Call is out of the money and expires worthless, and the short stockposition remains intact. The effective sale price of the short stock position in this example is $97, which is calculated by subtracting the costof 3.00 of the put from the short sale price of the stock of $100. Thus,with the stock price below the strike price at expiration, the syntheticlong put position described in Table 5-5 and Figure 5-5 becomes areal short stock position at an effective price of $97—the same resultas buying a real 100 Put for 3.00 and exercising it.In the third outcome, the stock price closes exactly at $100 at expiration, the long 100 Call expires worthless, and the short stock position remains intact. However, if the short stock were covered at $100after the call expires worthless, then the result would be a loss of 3.00and no position other than the $100 cash reserve—the same result asbuying a 100 Put at 3.00 and holding a cash reserve of $100; at expiration, the put expires worthless, and the cash reserve remains intact.The conclusion is that the two-part position of short stock and longcall behaves exactly the same as a real long put position. It thereforedeserves its name, synthetic long put.
Synthetic Short PutThe last synthetic position, the synthetic short put, is created withlong stock and a short call on a share-for-share basis. Table 5-6 andFigure 5-6 illustrate that long stock at $100 and a short 100 Call at3.00 are equivalent to a short 100 Put at 3.00. Table 5-6 shows theproﬁt-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 5-6 graphs the components andthe combined position.
Synthetic Relationships • 149
Row 4 in Table 5-6 assumes a stock price of $105 at expiration (column 1). The stock purchased at $100 makes a proﬁt of 5.00 per share(column 2), and the 100 Call sold at 3.00 incurs a loss of 2.00 pershare (column 3). Subtracting the call loss from the stock proﬁt yieldsa net proﬁt of 3.00 per share (column 4), which is the same proﬁt pershare that would be earned had a 100 Put been sold at 3.00 per share(column 5). Any row in Table 5-6 proves that the combination of thelong stock and short call in column 4 is equal to selling a 100 Put at3.00 in column 5.Table 5-6
Synthetic Short Put: Long Stock at 100 and Short 100 Call at 3.00Compared with Short 100 Put at 3.00Col 1
Col 2
Stock Priceat Expiration
Long Stock@ 100
9095100105110
10.005.00-05.0010.00
Row 1Row 2Row 3Row 4Row 5
Col 3
Col 4
Short 100 CombinedCall @ 3.00P/(L)3.003.003.002.007.00
7.002.003.003.003.00
Col 5Short 100Put @ 3.007.002.003.003.003.00
10
P/(L)
50–5–10
95
100
105
Stock PriceLong Stock @ 100Figure 5-6
Short100 Call @ 3
Short 100 Put @ 3
Synthetic Short Put = Long Stock and Short Call
150 • Trading Options As a Professional
Synthetic Short Put—Mechanics at ExpirationAs with all the other synthetic positions, 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 put positionresults in the same position, with the same proﬁt or loss, as if a real100 Put had been sold at 3.00 per share.When the stock price closes above $100 at expiration, the short 100Call is in the money and is assigned. Assignment of a short call createsa stock sale transaction, which sells the long stock. The effective priceof selling stock in this example is $103 because the premium receivedfor the call is added to the strike price of 100. Thus, with the stock priceabove the strike price at expiration, the synthetic short put positiondescribed in Table 5-6 and Figure 5-6 results in a proﬁt of 3.00 and nostock position, just as a real short 100 Put sold at 3.00 would expire andleave no position.If the stock price falls below $100 at expiration, then the short 100Call is out of the money and expires worthless, and the long stock position remains intact. The effective purchase price of the long stockposition in this example is $97, because the call premium received of3.00 is substracted from the purchase price fo the stock of $100. Thus,with the stock price below the strike price at expiration, the syntheticshort put position described in Table 5-6 and Figure 5-6 becomes areal long stock position at an effective price of $97—the same resultas selling a real 100 Put at 3.00 and being assigned.In the third outcome, the stock price closes exactly at $100 at expiration, the 100 short Call expires worthless, and the long stock position remains intact. However, if the stock were sold at $100 after thecall expires worthless, then the result would be a proﬁt of 3.00 fromthe short call and no position other than the cash reserve of $100. Thisis the same result as selling a 100 Put at 3.00 and holding a cashreserve of $100; at expiration, the put expires worthless, and the cashreserve remains intact.
Synthetic Relationships • 151
The conclusion is that the two-part position of long stock and shortcall behaves exactly the same as a real short put position. It thereforedeserves its name, synthetic short put.
When Stock Price ≠ Strike PriceTables 5-1 through 5-6 and Figures 5-1 through 5-6 assumed that thestock price and the strike prices of the call and put were all 100. Inthe real world, however, the stock price is rarely equal to the strikeprice of the options. If the stock price were different in the precedingexamples, the call and put prices also would vary. The resulting equivalencies, however, are the same! Table 5-7 and Figure 5-7 illustrate areal long stock position and a synthetic long stock position, assuminga stock price of $103, a 100 Call price of 4.50, and a 100 Put price of1.50. In every row of Table 5-7, the proﬁt or loss of the synthetic longstock position summarized in column 4 equals the proﬁt or loss of thereal long stock position in column 5. The price differences do not matter: The two-part position of a long 100 Call at 4.50 and a short 100Put at 1.50 is equal to the long stock at $103.
Table 5-7
Synthetic Long Stock When Stock Price ≠ Strike Price: Long 100Call at 4.50 and Short 100 Put at 1.50 Compared with Long Stockat 103.00Col 1
Col 2
Stock PriceLong 100at Expiration Call @ 4.50Row 1Row 2Row 3Row 4Row 5
95100103105110
4.504.501.500.505.50
Col 3
Col 4
Col 5
Short 100Put @ 1.50
CombinedP/(L)
Long Stock@ 103
3.501.501.501.501.50
8.003.00-02.007.00
8.003.00-02.007.00
152 • Trading Options As a Professional
10
P/(L)
50–5–1095
100
Long 100 Call @ 4.50
105
Stock PriceShort 100 Put @ 1.50
Long Stock @103
Figure 5-7
Synthetic Long Stock: Stock Price <>Strike Price
Table 5-8
Synthetic Long Call When Stock Price ≠ Strike Price: Long 100Stock at 97.00 and Long 100 Put at 5.50 Compared with Long 100Call at 2.50
Row 1Row 2Row 3Row 4Row 5
Col 1
Col 2
Col 3
Col 4
Col 5
Stock Priceat Expiration
Long Stock@ 97
Long 100Put @ 5.50
CombinedP/(L)
Long 100Call @ 2.50
909597100105
7.002.00-03.008.00
4.500.502.505.505.50
2.502.502.502.502.50
2.502.502.502.502.50
Table 5-8 and Figure 5-8 present a comparison of a long 100 Calland its synthetic equivalent assuming a stock price of $97, a 100 Callprice of 2.50, and a 100 Put price of 5.50. As in all the other examples,the proﬁt or loss of the synthetic long call summarized in column 4always equals the proﬁt or loss of the real long call in column 5. Asexplained next, all six synthetic relationships are related in the sameway to their corresponding real positions through the put-call parityequation.
Synthetic Relationships • 153
10
P/(L)
50–5–1095
100
105
Stock PriceLong Stock @ 97Figure 5-8
Long 100 Put @ 5.50
Long 100 Call @ 2.50
Synthetic Long Call: Stock Price <>Strike Price
The Put-Call Parity EquationSynthetic positions exist because of the put-call parity relationshipdeﬁned in line 1 of Table 5-9 as follows:Stock  call putwhere means “long” and means “short.”This put-call parity equation can be read as “long stock equals longcall plus short put.” The assumptions of Table 5-9 are that thecall and put have the same underlying, the same strike price, and thesame expiration date; that the interest rate is zero; and that there areno dividends.Lines 2 through 6 in Table 5-9 illustrate that the other ﬁve syntheticrelationships can be derived from the ﬁrst relationship. They follow algebraically from the basic equation in line 1. Consider line 2, in which“put” is added to both sides of the equation in line 1. The result is“Stock put  call” or, in words, “Long stock plus long put equalslong call.” Table 5-9 continues with lines 3 through 6, in which eachof the remaining synthetic relationships is expressed as an equation.
154 • Trading Options As a Professional
Table 5-9123456
The Put-Call Parity Equation and Derived Variations
Stock  call – putBasic put/call parity equation(Long stock equals long call and short put.)Stock  put   callAdd put to both sides of 1.(Long call equals long stock and long put.)Put  call – stockSubtract stock from both sides of 2.(Long put equals long call and short stock.)Put – call  – stockSubtract call from both sides of 3.(Short stock equals long put and short call.)– Call  – stock – putSubtract put from both sides of 4.(Short call equals short stock and short put.)– Call  stock  – putAdd stock to both sides of 5.(Short put equals long stock and short call.)
Equality of Call and Put Time PremiumsThe common element in the examples presented in Tables 5-1through 5-8 and Figures 5-1 through 5-8 is the equality of call and puttime premiums. As explained in Chapter 1, time premium (or timevalue) is the portion of an option’s price in excess of intrinsic value, ifany. In tables and ﬁgures 5-1 through 5-6, the prices of the 100 Calland 100 Put were both 3 and consisted entirely of time value becausethe stock price was $100. Therefore, the time premiums of theseoptions were equal.In Table 5-7 and Figure 5-7, the stock price is $103, the price of the100 Call is 4.50, and the price of the 100 Put is 1.50. The price ofthe 100 Call consists of 3.00 of intrinsic value and 1.50 of time value.The 100 Put is out of the money, so its entire price of 1.50 consists oftime value. Thus the time premiums of these options are also equal.In Table 5-8 and Figure 5-8, the stock price is $97, the price of the100 Call is 2.50, and the price of the 100 Put is 5.50. The 100 Put,being in the money, has 3.00 of intrinsic value and 2.50 of time value.The price of the out-of-the-money 100 Call of 2.50 consists entirelyof time value, which, again, equals the time value of the 100 Put.Figure 5-9 illustrates graphically how the time values of the 100 Calland 100 Put are equal in the example in Table 5-8 and Figure 5-8.
Synthetic Relationships • 155
Call Price
OptionPrice
StockPrice
3
103100Call2.50
21
IntrinsicValue3.00
234Put Price
101Strike Price
99100Put5.50
TimeValue2.50
9897
Stock Price
96
5
95
6
95
Stock Price100 Call100 PutFigure 5-9
102
100
01
TimeValue2.50
97.002.505.50
Equality of Time Premiums
Applying the Effective Stock Price ConceptThe effective stock price concept is useful in calculating syntheticprices. The price of a call increases the effective stock price becauseif a call is exercised or assigned, the effective purchase or sale price ofthe stock is the strike price plus the call price. The price of a put, however, decreases the effective stock price because the effective purchaseor sale price of the stock for an exercised or assigned put is the strikeprice minus the put price.When the interest rate and dividends are assumed to be zero, thesynthetic stock price is simply the effective stock price. Consider theprices in Tables 5-1 and 5-2 and Figures 5-1 and 5-2—a stock price