48 lines
2.0 KiB
Plaintext
48 lines
2.0 KiB
Plaintext
754 Part VI: Measuring and Trading Volatility
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FIGURE 37-1.
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Theoretical option prices at differing implied
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volatilities (6-month calls).
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80
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70
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Q) 60
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(.)
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·;:::
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Cl.. 50
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C:
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0
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·a 40
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0
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30
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20
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10
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Stock Price
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60 80 100 C 120 140
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_JY.._
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170%
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140%
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110%
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80%
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50%
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20%
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The bottom line in Figure 37-1 (where implied volatility= 20%) has a distinct
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curvature to it when the stock price is between about 80 and 120. Thus the delta
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ranges from a fairly low number (when the stock is near 80) to a rather high number
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(when the stock is near 120). Now look at the top line on the chart, where implied
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volatility= 170%. It's almost a straight line from the lower left to the upper right! The
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slope of a straight line is constant. This tells us that the delta (which is the slope)
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barely changes for such an expensive option - whether the stock is trading at 60 or
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it's trading at 150! That fact alone is usually surprising to many.
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In addition, the value of this delta can be measured: It's 0. 70 or higher from a
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stock price of 80 all the way up to 150. Among other things, this means that an out~
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of-the-money option that has extremely high implied volatility has a fairly high delta
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- and can be expected to mirror stock price movements more closely than one might
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think, were he not privy to the delta.
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Figure 37-2 follows through on this concept, showing how the delta of an option
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varies with implied volatility. From this chart, it is clear how much the delta of an
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option varies when the implied volatility is 20%, as compared to how little it varies
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when implied volatility is extremely high.
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That data is interesting enough by itself, but it becomes even more thought-pro
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voking when one considers that a change in the implied volatility of his option (vega)
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also can mean a significant change in the delta of the option. In one sense, it explains
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why, in the first chart (Figure 37-1), the stock could rise 9 points and yet the option
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holder made nothing, because implied volatility declined from 170% to 140%. |