Lecture 12 Tutorial Questions - Solutions(1).pdf

B a long position in 5000 traded options will give a

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b) A long position in 5,000 traded options will give a vega-neutral portfolio since the long position has a vega of 5,000 x 0.8 = +4,000. However, the delta of the whole portfolio (including traded options) is then 450 + (5,000 x 0.6) = 2,550. Hence, in addition to the 5,000 traded options, a short position of 2,550 in sterling is necessary so that the portfolio is both vega and delta neutral. Problem 17.27 Let w 1 be the position in the first traded option and w 2 be the position in the second traded option. To make the portfolio both gamma neutral and vega neutral we require 1 2 6 000 1 5 0 5 w w     1 2 4 000 0 8 0 6 w w     The solution to these equations is w 1 =3,200 and w 2 = 2,400. The delta of the whole portfolio is now 450 3 200 0 6 2 400 0 1 1 710           This can be neutralised by taking a short position of 1,710 in sterling. In conclusion, the portfolio can be made delta, gamma and vega neutral by taking a long position in 3,200 of the first traded option, a long position in 2,400 of the second traded option and a short position of 1,710 in sterling.
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