37 lines
2.2 KiB
Plaintext
37 lines
2.2 KiB
Plaintext
Chapter 40: Advanced Concepts 887
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will necessarily be used to make these projections. As was shown earlier, if there is a
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distortion in the current implied volatilities of the options involved in the position,
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the strategist should use the current implieds as input to the model for future option
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price projections. If he does not, the position may look overly attractive if expensive
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options are being sold or cheap ones are being bought. A truer profit picture is
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obtained by propagating the current implied volatility structure into the near future.
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Using an example similar to the previous one a ratio spread using short stock
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to make it delta neutral - the concepts will be described.
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Initial Position. XYZ is at 60. The January 70 calls, which have three months
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until expiration, are expensive with respect to the January 60 calls. A strategist
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expects this discrepancy to disappear when the implied volatility of XYZ options
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decreases. He therefore established the following position, which is both gamma
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and delta neutral.
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Position Delta Gamma
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Long 100 January 60 calls 0.57 0.0723
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Short 240 January 70 calls 0.20 0.0298
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Short 800 XYZ
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The risk measures for the entire position are:
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Position delta: -38 shares (virtually delta neutral)
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Position gamma: + 7 shares (gamma neutral)
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Position theta: + $263
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Position vega: -$827
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Theta Vega
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-0.020 0.109
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-0.019 0.080
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Thus, the position is both gamma and delta neutral. Moreover, it has the attrac
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tive feature of making $263 per day because of the positive theta. Finally, as was the
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intention of the spreader, it will make money if the volatility of XYZ declines: $827
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for each percentage point decrease in implied volatility. Two equations in two
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unknowns (gamma and vega) were solved to obtain the quantities to buy and sell. The
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resulting position delta was neutralized by selling 800 XYZ.
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The following analyses will assume that the relative expensiveness of the April
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70 calls persists. These are the calls that were sold in the position. If that overpricing
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should disappear, the spread would look more favorable, but there is no guarantee
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that they will cheapen - especially over a short time period such as one or two weeks.
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How would the position look in 7 days at the stock prices determined above? |