39 lines
2.5 KiB
Plaintext
39 lines
2.5 KiB
Plaintext
Chapter 38: The Distribution of Stock Prices 805
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ing price of the naked put being sold is 550. The resulting probabilities might be
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something like this:
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Scenario Actual Probability of Occurrence
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1 . $OEX never falls below 550
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2. $OEX falls below 550 and remains there
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3. $OEX falls below 550 but rallies later
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67%
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19%
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14%
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The probabilities stated above are the "real" probabilities of the three various
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scenarios occurring. However, if one were using the simple probability calculator
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presented above, he would only have the following information:
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Probability of $OEX being above 550 at expiration: 81 %
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Probability of $OEX being below 550 at expiration: 19%
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So, with the simple calculator, it looks like there's an 81 % chance of a worry-free
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trade. Just sit back and relax and let the option expire worthless. However, in real
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life - as shown by the previous set of probabilities, there's only a 67% chance of a
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worry-free trade. The difference - the other 14% - is the probability of the third
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scenario occurring ($OEX falls below 550, but rallies back above it by expiration).
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The simple probability calculator doesn't account for that scenario at all.
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Hence, most serious traders don't use the simple model. Does that mean it's not
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useful at all? No, it is certainly viable as a comparative tool; for example, to compare
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the chances of the $OEX put expiring worthless versus those of another put sale
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being considered, perhaps something in a stock option. However, better analyses can
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be undertaken.
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Before leaving the scenario of the simple probability calculator, one more point
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should be made. It has been mentioned earlier in this book that the delta of an option
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is actually a fairly good estimate of the probability of the option being in-the-money
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at its expiration date. Thus, the delta and the simple endpoint probability calculator
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shown above attempt to convey the same information to a trader. In reality, because
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of the fact that implied volatility might be different for various strikes (a volatility
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skew), especially in index options, the delta of the option might not agree exactly with
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the probability calculator. Even so, the delta is a quick and dirty way of estimating the
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probability of the stock being above the strike price (in the case of call options) or
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below the strike price (in the case of put options) at expiration.
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THE nEVER" CALCULATOR
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Having seen the frailties of the endpoint calculator, the next step is to try to design a
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calculator that can estimate the probability of the stock ever hitting the target price(s) |