46 lines
1.8 KiB
Plaintext
46 lines
1.8 KiB
Plaintext
894 Part VI: Measuring and Trading Volatility
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quick changes in volatility. In order to quantify the statement that he "wants to be
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gamma long," let us assume that he wants to be gamma long 1,000 shares or 10 con
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tracts.
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It is known that delta can always be neutralized last, so let us concentrate on the
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other two variables first. The two equations below are used to determine the quanti
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ties to buy in order to make gamma long and vega neutral:
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0.0510x + 0.0306y = 10 (gamma, expressed in# of contracts)
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0.089x + 0.147y = 0 (vega)
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The solution to these equations is:
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X = 308, y = -186
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Thus, one would buy 308 March 60 calls and would sell 186 June 60 calls. This is the
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reverse calendar spread that was discussed: Near-term calls are bought and longer
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term calls are sold.
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Finally, the delta must be neutralized. To do this, calculate the position delta
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using the quantities just determined:
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Position delta= 0.54 x 308 - 0.57 x 186 = 60.30
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So, the position is long 60 contracts, or 6,000 shares. It can be made delta neutral by
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selling short 6,000 shares of XYZ.
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The overall position would look like this:
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Position
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Short 6,000 XYZ
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Long 308 March 60 calls
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Short 186 June 60 calls
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Its risk measurements are:
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Delta
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1.00
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0.54
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0.57
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Position delta: long 30 shares (neutral)
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Position vega: $7 (neutral)
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Position gamma: long 1,001 shares
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Gamma
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0
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0.0510
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0.0306
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Vega
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0
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0.089
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0.147
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This position then satisfies the initial objectives of wanting to be gamma long
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1,000 shares, but delta and vega neutral.
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Finally, note that theta = -$625. The position will lose $625 per day from time
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decay.
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The strategist must go further than this analysis, especially if one is dealing with
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positions that are not simple constructions. He should calculate a profit picture as |