52 lines
2.0 KiB
Plaintext
52 lines
2.0 KiB
Plaintext
Chapter 37: How Volatility Affeds Popular Strategies
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TABLE 37-3
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Implied
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Stock Price Volatility
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50 10%
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30%
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50%
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70%
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100%
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150%
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200%
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Theoretical
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Coll Price
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1.34
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3.31
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5.28
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7.25
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10.16
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14.90
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19.41
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753
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Vega
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0.097
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0.099
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0.099
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0.098
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0.096
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0.093
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0.088
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of a 6-month call option with differing implied volatilities. Suppose one buys an
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option that currently has implied volatility of 170% (the top curve on the graph).
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Later, investor perceptions of volatility diminish, and the option is trading with an
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implied volatility of 140%. That means that the option is now "residing" on the sec
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ond curve from the top of the list. Judging from the general distance between those
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two curves, the option has probably lost between 5 and 8 points of value due to the
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drop in implied volatility.
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Here's another way to think about it. Again, suppose one buys an at-the-money
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option (stock price = 100) when its implied volatility is 170%. That option value is
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marked as point A on the graph in Figure 37-1. Later, the option's implied volatility
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drops to 140%. How much does the stock have to rise in order to overcome the loss
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of implied volatility? The horizontal line from point A to point B shows that the
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option value is the same on each line. Then, dropping a vertical line from B down to
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point C, we see that point C is at a stock price of about 109. Thus, the stock would
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have to rise 9 points just to keep the option value constant, if implied volatility drops
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from 170% to 140%.
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IMPLIED VOLATILITY AND DELTA
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Figure 37-1 shows another rather unusual effect: When implied volatility gets very
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high, the delta of the option doesn't change much. Simplistically, the delta of an
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option measures how much the option changes in price when the stock moves one
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point. Mathematically, the delta is the first partial derivative of the option model with
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respect to stock price. Geometrically, that means that the delta of an option is the
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slope of a line drawn tangent to the curve in the preceding chart. |