Chapter 28: Mathematical Applications 479 
Theoretical synthetic Theoretical Strike Stock D" .d d = + - + 1vi en s put price call price price price 
When the ranking analysis is performed, very few synthetic puts will appear as 
attractive put buys. This is because, when the customer buys a synthetic put, he must 
advance the full cost of the dividend, but receives no offsetting cost reduction for the 
credit being earned by the short stock position. Consequently, synthetic puts are 
always more expensive, on a relative basis, than are listed puts. However, if one is par­
ticularly bearish on a stock that has no listed puts, a synthetic put may still prove to 
be a worthwhile investment. The recommended analysis can give him a feeling for 
the reward and risk potential of the investment. 
CALENDAR SPREADS 
The pricing nwdel can help in determining which neutral calendar spreads are nwst 
attractive. Recall that in a neutral calendar spread, one is selling a near-term call and 
buying a longer-term call, when the stock is relatively close to the striking price of the 
calls. The object of the spread is to capture the time decay differential between the 
two options. The neutral calendar spread is normally closed when the near-term 
option expires. The pricing model can aid the spreader by estimating what the prof­
it potential of the spread is, as well as helping in the determination of the break-even 
points of the position at near-term expiration. 
To determine the maximum profit potential of the spread, assume that the near­
term call expires worthless and use the pricing model to estimate the value of the 
longer-term call with the stock exactly at the striking price. Since commission costs 
are relatively large in spread transactions, it would be best to have the computations 
include commissions. Calculating a second profit potential is sometimes useful as 
well the profit if unchanged. To determine how much profit would be made if the 
stock were unchanged at near-term expiration, assume that the spread is closed with 
the near-term call equal to its intrinsic value (zero if the stock is currently below the 
strike, or the difference between the stock price and the strike if the stock is initial­
ly above the strike). Then use the pricing model to estimate the value of the longer­
term call, which will then have three or six months of life remaining, with the stock 
unchanged. The resulting differential between the near-term call's intrinsic value and 
the estimated value of the longer-term call is an estimate of the price at which the 
spread could be liquidated. The profit, of course, is that differential minus the cur­
rent (initial) differential, less commissions. 
In the earlier discussion of calendar spreads, it was pointed out that there is 
both an upside break-even point and a downside break-even point at near-term expi­
ration. These break-even points can be estimated with the use of the pricing model.