33 lines
2.3 KiB
Plaintext
33 lines
2.3 KiB
Plaintext
The Intelligent Investor’s Guide to Option Pricing • 67
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At time A for the OTM option, we see that there is a bit of the range of
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exposure contained within the cone; however, after some time has passed
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and we are at time B, none of the range of exposure is contained within
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the BSM cone. In contrast, at times A and B for the ITM option, the entire
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range of exposure is contained within the BSM cone. Granted, the area of
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the range of exposure is not as great at time B as it was at time A, but still,
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what there is of the area is completely contained within the cone.
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Theoretically, time decay is a constant thing, but sometimes actual
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market pricing does not conform well to theory, especially for thinly traded
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options. For example, you might not see any change in the price of an option
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for a few days and then see the quoted price suddenly fall by a nickel even
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though the stock price has not changed much. This is a function of the way
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prices are quoted—often moving in 5-cent increments rather than in 1-cent
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increments—and lack of “interest” in the option as measured by liquidity.
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Changing Other Assumptions
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The other input assumptions for the BSM (stock market drift and dividend
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yield) have very small effects on the range of predicted future outcomes in
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what I would call “normal” economic circumstances. The reason for this is
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that these assumptions do not change the width of the BSM cone but rather
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change the tilt of the forward stock price line.
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Remember that the effect of raising interest rates by a few points is
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simply to tilt the forward stock price line up by a few degrees; increasing
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your dividend assumptions has the opposite effect. As long as interest rates
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and dividend yields stay within typical limits, you hardly see a difference in
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predicted ranges (or option prices) on the basis of a change in these variables.
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Simultaneous Changes in Variables
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In all the preceding examples, we have held all variables but one constant
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and seen how the option price changes with a change in the one “free”
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variable. The thing that takes some time to get used to when one is first
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dealing with options is that, in fact, the variables don’t all hold still when
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another variable changes. The two biggest determinants of option price
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are, as we’ve seen, the strike–stock price ratio and the forward volatility |