34 lines
2.3 KiB
Plaintext
34 lines
2.3 KiB
Plaintext
Chapter 28: Mathematical Applications 477
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upward potential was 65/s points, while the downward potential is about 5¾ points.
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This difference is due to the use of the lognormal distribution.
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Step 8: Using the Black-Scholes model, one could estimate that the XYZ
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January 40 call would be worth about 11/s if XYZ were at 35¼ in 90 days.
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Step 9: The risk potential in the January 40 call would be:
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. 4- l1/s 27/s Percent nsk = --- = - 72% 4 4
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Step 10: The reward/risk ratio is merely the percentage reward divided by the per
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centage risk:
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Reward/risk ratio = l03% = 1.43 72%
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Step 11: This analysis would be repeated for all XYZ options, and then for all other
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optionable stocks. The less aggressive call purchases would be ranked by their
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reward/risk ratios, with higher ratios representing more attractive purchases. More
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aggressive purchases would be ranked by the potential rewards only (step 5).
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This completes the call buying example. Before leaving this section, it should be
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noted that the assumption of ranking the purchases after one full standard deviation
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movement by the underlying stock is probably excessive. A more moderate assump
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tion would be that the stock might be able to move . 7 standard deviation. There is
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about a 25% expected chance that a stock could move up at least . 7 standard devia
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tion at the end of a fixed time period.
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PRICING A PUT OPTION
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Theoretical models for pricing put options have been derived; that is, ones that are
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separate from call pricing models. Black and Scholes presented such a model in their
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original paper. However, as has been demonstrated, there is a relationship between
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put and call prices in the listed option market due to the conversion and reversal
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strategies.
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One could use the ba,sic call pricing rrwdel for the purpose of predicting put
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prices if he a,ssumes that arbitrageurs will efficiently influence the market via con
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versions. Theoreticians will argue that such a method of pricing puts assumes that the
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arbitrage process is always present and works efficiently, and that this is not true. The
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"conversion efficiency" assumption could be a serious fault if one were trying to
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determine the exact overpriced or underpriced nature of the put option. However, if
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one is merely comparing various put strategies under constant assumptions, the arbi
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trage model for pricing puts works quite well. |