36 lines
2.1 KiB
Plaintext
36 lines
2.1 KiB
Plaintext
752 Part VI: Measuring and Trading Volatility
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The above example assumed that the stock was making instantaneous changes
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in price. In reality, of course, time would be passing as well, and that affects the vega
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too. Table 37-2 shows how the vega changes when time changes, all other factors
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being equal.
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Example: In this example, the following items are held fixed: stock price (50), strike
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price (50), implied volatility (70%), risk-free interest rate (5%), and dividend\(0). But
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now, we let time fluctuate.
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Table 37-2 clearly shows that the passage of time results not only in a decreas
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ing call price, but in a decreasing vega as well. This makes sense, of course, since one
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cannot expect an increase in implied volatility to have much of an effect on a very
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short-term option - certainly not to the extent that it would affect a LEAPS option.
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Some readers might be wondering how changes in implied volatility itself would
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affect the vega. This might be called the "vega of the vega," although I've never actu
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ally heard it referred to in that manner. The next table explores that concept.
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Example: Again, some factors will be kept constant - the stock price (50), the time
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to July expiration (3 months), the risk-free interest rate (5%), and the dividend (0).
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Table 37-3 allows implied volatility to fluctuate and shows what the theoretical price
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of a July 50 call would be, as well as its vega, at those volatilities.
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Thus, Table 37-3 shows that vega is surprisingly constant over a wide range of
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implied volatilities. That's the real reason why no one bothers with "vega of the vega."
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Vega begins to decline only if implied volatility gets exceedingly high, and implied
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volatilities of that magnitude are relatively rare.
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One can also compute the distance a stock would need to rise in order to over
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come a decrease in volatility. Consider Figure 37-1, which shows the theoretical price
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TABLE 37-2
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Implied Time Theoretical
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Stock Price Volatility Remaining Call Price Vega
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50 70% One year 14.60 0.182
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Six months 10.32 0.135
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Three months 7.25 0.098
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Two months 5.87 0.080
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One month 4.16 0.058
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Two weeks 2.87 0.039
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One week 1.96 0.028
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One day 0.73 0.010 |