23 lines
1.4 KiB
Plaintext
23 lines
1.4 KiB
Plaintext
trading days per year is 256, because its square root is a round number: 16.
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The formula is
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For example, a $100 stock that has an at-the-money (ATM) call trading at
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a 32 percent volatility implies that there is about a 68 percent chance that
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the underlying stock will be between $68 and $132 in one year’s time—
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that’s $100 ± ($100 × 0.32). The estimation for the market’s expectation for
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the volatility of the stock for one day in terms of standard deviation as a
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percentage of the price of the underlying is computed as follows:
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In one day’s time, based on an IV of 32 percent, there is a 68 percent
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chance of the stock’s being within 2 percent of the stock price—that’s
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between $98 and $102.
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There may be times when it is helpful for traders to have a volatility
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estimation for a period of time longer than one day—a week or a month, for
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example. This can be accomplished by multiplying the one-day volatility by
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the square root of the number of trading days in the relevant period. The
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equation is as follows:
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If the period in question is one month and there are 22 business days
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remaining in that month, the same $100 stock with the ATM call trading at a
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32 percent implied volatility would have a one-month volatility of 9.38
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percent.
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Based on this calculation for one month, it can be estimated that there is a
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68 percent chance of the stock’s closing between $90.62 and $109.38 based
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on an IV of 32 percent. |