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14 Part I: Basic Properties ol Stodc Options
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stock has the ability to move a relatively large distance upward, buyers of the calls are
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willing to pay higher prices for the calls - and sellers demand them as well. For exam
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ple, if AT&T and Xerox sell for the same price (as they have been known to do), the
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Xerox calls would be more highly priced than the AT&T calls because Xerox is a more
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volatile stock than AT&T.
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The interplay of the four major variables - stock price, striking price, time, and
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volatility can be quite complex. While a rising stock price (for example) is directing
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the price of a call upward, decreasing time may be simultaneously driving the price
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in the opposite direction. Thus, the purchaser of an out-of-the-money call may wind
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up with a loss even after a rise in price by the underlying stock, because time has
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eroded the call value.
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THE TWO MINOR DETERMINANTS
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The Risk-Free Interest Rate. This rate is generally construed as the current
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rate of 90-day Treasury bills. Higher interest rates imply slightly higher option pre
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miums, while lower rates imply lower premiums. Although members of the financial
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community disagree as to the extent that interest rates actually affect option price,
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they remain a factor in most mathematical models used for pricing options. (These
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models are covered much later in this book.)
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The Cash Dividend Rate of the Underlying Stock. Though not clas
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sified as a major determinant in option prices, this rate can be especially impor
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tant to the writer (seller) of an option. If the underlying stock pays no dividends
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at all, then a call option's worth is strictly a function of the other five items.
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Dividends, however, tend to lower call option premiums: The larger the dividend
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of the underlying common stock, the lower the price of its call options. One of
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the most influential factors in keeping option premiums low on high-yielding
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stock is the yield itself.
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Example: XYZ is a relatively low-priced stock with low volatility selling for $25 per
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share. It pays a large annual dividend of $2 per share in four quarterly payments of
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$.50 each. What is a fair price of an XYZ call with striking price 25?
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A prospective buyer of XYZ options is determined to figure out a fair price. In
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six months XYZ will pay $1 per share in dividends, and the stock price will thus be
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reduced by $1 per share when it goes ex-dividend over that time period. In that case,
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if XYZ's price remains unchanged except for the ex-dividend reductions, it will then
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be $24. Moreover, since XYZ is a nonvolatile stock, it may not readily climb back to
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25 after the ex-dividend reductions. Therefore, the call buyer makes a low bid - even
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