41 lines
2.7 KiB
Plaintext
41 lines
2.7 KiB
Plaintext
482
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A Complete Guide to the Futures mArket
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table 34.2 Option prices as a Function of V olatility in
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e-Mini S&p 500 Futures pricesa
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annualized V olatility put or Call premium
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10 22.88 ($1,144)
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20 45.75 ($2,288)
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30 68.62 ($3,431)
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40 91.46 ($4,573)
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50 114.29 ($5,715)
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a At-the-money options at a strike price of 2000 with 30 days to expiration.
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8 James Bowe, Option Strategies T rading Handbook (New Y ork, NY: Coffee, Sugar, and Cocoa exchange, 1983).
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assumed to be a function of the square root of time. (This relationship is a consequence of the
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typical assumption regarding the shape of the probability curve for prices of the underlying
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futures contract.) Thus, an option with nine months until expiration would have 1.5 times the
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time value of a four-month option with the same strike price
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(; ;. )93 42 32 15== ÷=
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and three times the time value of a one-month option (; ;)93 11 31 3== ÷= .
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3. V olatility. Time value will vary directly with the estimated volatility of the underlying futures
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contract for the remaining lifespan of the option. This relationship is the result of the fact that
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greater volatility raises the probability the intrinsic value will increase by any specified amount
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prior to expiration. In other words, the greater the volatility, the larger the probable range of
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futures prices. As Table 34.2 shows, volatility has a strong impact on theoretical option pre-
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mium values.
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Although volatility is an extremely important factor in determining option premium values,
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it should be stressed that the future volatility of the underlying futures contract is never pre-
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cisely known until after the fact. (In contrast, the time remaining until expiration and the rela -
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tionship between the current price of futures and the strike price can be exactly specified at any
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juncture.) Thus, volatility must always be estimated on the basis of historical volatility data. As
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will be explained, this factor is crucial in explaining the deviation between theoretical and actual
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premium values.
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4. Interest rates. The effect of interest rates on option premiums is considerably smaller than
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any of the above three factors. The specific nature of the relationship between interest rates and
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premiums was succinctly summarized by James Bowe
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8:
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The effect of interest rates is complicated because changes in rates affect not only the
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underlying value of the option, but the futures price as well. Taking it in steps, a buyer
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of any given option must pay the premium up front, and of course the seller receives
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the money. If interest rates go up and everything else stays constant, the opportunity
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cost to the option buyer of giving up the use of his money increases, and so he is will-
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ing to bid less. Conversely, the seller of options can make more on the premiums by |