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