478 Part IV: Additional Considerations 
The listed put' s price can be estimated by using the call pricing model and the 
arbitrage formula. Recall that the arbitrageur must include the cost of carrying the 
position as well as the dividends to be received. 
Theoretical Theoretical Strike Stock Carrying n· 'd d = + - - + IVI en s put call price price price cost 
The "theoretical call price" is obtained from the Black-Scholes model. The carrying 
cost is the cost of money (interest rate) times the striking price, multiplied by the 
time to expiration. Recall that this is the approximation formula for carrying cost (see 
Chapter 27 for comments on present value and compounding). Consequently, ifXYZ 
were at 41 and a 6-month January 40 call option were valued at 4 points by the 
Black-Scholes model, the theoretical put price could be estimated. Assume that the 
cost of money interest rate is 10% annually, and that the stock will pay $.50 in divi­
dends in 6 months (t = ½ year). 
Theoretical put price = 4 + 40 - 41- (.10 x 40 x ½) + .50 
=3-2+½ 
=l½ 
This means that if the call could be sold for 4 points, the arbitrageur would be will­
ing to pay up to 1 ½ points for the put to establish a conversion. The arbitrageur's 
price is used as the theoretical listed put price estimate. 
PUT BUYING 
Put option purchases can be ranked in a manner very similar to that described for call 
option buying. Reward opportunities occur when the stock falls in accordance with 
its volatility. An upward stock movement represents risk for the put buyer. All of the 
11 steps in the previous section on call buying are applicable to put buying. The pric­
ing of the put necessary for steps 4 and 8 is done in accordance with the arbitrage 
model just presented. 
If an underlying stock does not have listed puts trading, the synthetic put can 
be considered. While all U.S.-listed stocks have both puts and calls at every strike, 
there are still situations with warrants, especially in foreign countries, that are appli­
cable to the following discussion. Recall that synthetic puts are created for customers 
by some brokerage houses. The brokerage sells the stock short and buys a call. The 
customer can purchase the synthetic put for the amount of the risk involved, plus any 
dividends to be paid by the underlying stock. The synthetic put pricing formula that 
would be used in steps 4 and 8 of the option buying analysis is exactly the same as the 
arbitrage model for listed puts, except that the carrying costs are omitted: