35 lines
1.6 KiB
Plaintext
35 lines
1.6 KiB
Plaintext
The Intelligent Investor’s Guide to Option Pricing • 65
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It is clear from the large area of the exposure range bordered by the
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BSM probability cone that this option will be fairly expensive.
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Let’s now look at an option struck at the same price on the same un-
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derlying equity but with only one year until expiration:
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Advanced Building Corp. (ABC)
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5/18/2012 5/20/2013 249 499 749 999
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100
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90
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80
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70
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60
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50
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40
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30
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20
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Date/Day Count
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Stock Price
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GREEN
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Consistent with our expectations, shortening the time to expiration
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to 365 days from 730 days does indeed change the likelihood as calculated
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by the BSM of a call option going above $60 from quite likely to just barely
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likely. Again, this can be confirmed visually by noting the much smaller
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area of the exposure range bounded by the BSM probability cone in the
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case of the one-year option versus the two-year one.
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Indeed, even without drawing two diagrams, we can see that the
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chance of this stock rising above $60 decreases the fewer days until expira-
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tion simply because the outline of the BSM probability cone cuts diagonal-
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ly through the exposure range. As the cone’s outline gets closer to the edge
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of the exposure range and finally falls below it, the perceived chance falls
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to 16 percent and then lower. We would expect, just by virtue of the cone’s
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shape, that options would lose value with the passage of time.
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This effect has a special name in the options world—time decay. Time
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decay means that even if neither a stock’s price nor its volatility change very
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much over the duration of an option contract, the value of that option will |