43 lines
2.0 KiB
Plaintext
43 lines
2.0 KiB
Plaintext
Chapter 37: How Volatility Affects Popular Strategies 779
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Example: Suppose that XYZ is trading at 100, and one is interested in a calendar
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spread in which an August (5-month) call is bought and a May (2-month) call is sold.
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For the purpose of this example, it will be assumed that these are both at-the-money
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options. First, the vegas of the two options will be examined, assuming that implied
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volatility is 40%:
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Stock: 100
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Implied Volatility:
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40% Option
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Sell May 100 call
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Buy August 1 00 call
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Theoretical Price
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6.91
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11.22
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Vega
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0.162
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0.251
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In theory, this spread should be worth 4.31 - the difference in the theoretical
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values. Perhaps more important, it has volatility exposure of 0.089 - the difference
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between the vega of the long call and that of the short call. Since vega is positive, this
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means that an increase in implied volatility will be beneficial to the spread. In other
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words, one can expect the spread to widen if implied volatility rises, and can expect
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the spread to shrink if implied volatility declines.
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The following table can also be constructed, showing the theoretical value of
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the spread at various levels of implied volatility. This table makes the assumption that
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very little time has passed ( only one week) before the implied volatility changes take
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place. It also assumes that the stock is still at 100.
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Stock Price: 100
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One week ofter the spread hos been established:
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Implied Volatility Theoretical Spread Value
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20% 2.58
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30% 3.52
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40% 4.46
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50% 5.40
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60% 6.33
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80% 8.16
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100% 12.92
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From the above data, it is quite obvious that implied volatility levels have a huge
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effect on the value of a calendar spread. The actual initial contribution of time decay
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is rather small in comparison. For example, note that if volatility remains unchanged
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at 40%, then the spread will have widened only slightly - to 4.46 from 4.31 - after
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the passage of one week's time. That is small in comparison to the changes dictated
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by volatility expansion or contraction. |