37 lines
2.5 KiB
Plaintext
37 lines
2.5 KiB
Plaintext
804 Part VI: Measuring and Trading Volatility
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If one is interested in computing the probability of the stock being above the
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given price, the formula is
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P (above) = 1 - P (below)
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In the above formula, Vt = v✓t where t is time to expiration in years and v is
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annual volatility, as usual.
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This formula is quite elementary for predictive purposes, and it is used by
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many traders. This calculator can be found for free at the Web site www.option
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strategist.com. Its main problem is that it gives the probability of the stock being
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above or below the target price at the end of the time period, t. That's not a totally
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realistic way of approaching probability analysis. Most option traders are very con
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cerned with what happens to their positions during the life of the option, not just at
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expiration.
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Example: suppose a trader is a seller of naked put options. He sells $OEX October
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550 puts naked, with $OEX currently trading at 600. He would not normally just walk
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away from this position until October expiration, because of the large risk involved
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with the sale of a naked option. There are essentially three scenarios that can occur:
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1. $OEX might never fall to 550 by expiration. In this case, he would have a
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very comfortable trade that was never in jeopardy, and the options would
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expire worthless.
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2. $OEX might fall below 550 and remain there until expiration. In this case,
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he would surely have a loss unless $OEX were just a tiny bit below 550.
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3. $OEX might fall below 550 at some time between when the trade was estab
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lished and when expiration occurred, but then subsequently rally back above
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550 by the time expiration arrived.
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An experienced option trader would almost certainly adjust if scenario 3 arose,
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in order to prevent large losses from occurring. He might roll his naked puts down
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and out to another strike, or he might just close them out altogether. However, it is
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unlikely that he would do nothing.
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The simple probability calculator formula shown above does not take into
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account the trader's third scenario. Since it is only concerned with where the stock is
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at expiration of the options, only scenarios 1 and 2 apply to it. Hence the usage of this
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simple calculator is not really descriptive of what might happen to a trade during its
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lifetime.
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Let's assign some numbers to the above trade, so that you might see the differ
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ence. Suppose that the volatility estimate is 25%, there are 30 days until expiration,
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and the prices are as stated in the previous example: $OEX is at 600, and the strik- |