33 lines
1.7 KiB
Plaintext
33 lines
1.7 KiB
Plaintext
884 Part VI: Measuring and Trading VolatiHty
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To answer the question, one must create two equations in two unknowns, x and
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y. The unknowns represent the quantities of options to be bought and sold, respec
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tively. The constants in the equations are taken from the table above.
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The first equation represents gamma neutral:
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0.045 X + 0.026 y = 0,
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where
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xis the number of April 50's in the spread and y is the number of April 60's. Note
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that the constants in the equation are the gammas of the two calls involved.
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The second equation represents the desired vega risk of making 2.5 points, or $250,
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if the volatility decreases:
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0.08 X + 0.06 y = - 2.5,
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where
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x and y are the same quantities as in the first equation, and the constants in this equa
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tion are the gammas of the options. Furthermore, note that the vega risk is negative,
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since the spreader wants to profit if volatility decreases.
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Solving the two equations in two unknowns by algebraic methods yields the fol
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lowing results:
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Equations:
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0.045 X + 0.026 y = 0
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0.08 X + 0.06 Y = - 2.5
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Solutions:
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X = 104.80
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y = -181.45
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This means that one would buy 105 April 50 calls, since x being positive means that
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the options would be bought. He would also sell 181 April 60 calls (y is negative,
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which implies that the calls would be sold). This is nearly the same ratio determined
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in the previous example. The quantities are slightly higher, since the vega here is
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-$250 instead of the -$238 achieved in the previous example.
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Finally, one would again determine the amount of stock to buy or sell to neu
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tralize the delta by computing the position delta:
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Position delta = 105 x 0.47 - 181 x 0.17 = 18.58
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Thus 1,858 shares of XYZ would be shorted to neutralize the position. |