Lecture 12 Tutorial Questions - Solutions(1).pdf

Writers position is highly negative and the delta is

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writer’s position is highly negative and the delta is zero, the option writer will lose money if there is a large movement (either up or down) in the asset price. The delta of zero means that the option writer s position is immunised against a small movement (either up or down) in the asset price.
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Problem 17.26 The delta of the portfolio is 1 000 0 50 500 0 80 2 000 ( 0 40) 500 0 70 450                The gamma of the portfolio is 1 000 2 2 500 0 6 2 000 1 3 500 1 8 6 000                  The vega of the portfolio is 1 000 1 8 500 0 2 2 000 0 7 500 1 4 4 000                  a) A long position in 4,000 traded options will give a gamma-neutral portfolio since the long position has a gamma of 4,000 x 1.5 = +6,000. However, the delta of the whole portfolio (including traded options) is now 450 + (4,000 x 0.6) = 1,950. Hence, in addition to the 4,000 traded options, a short position of 1,950 in sterling is necessary so that the portfolio is both gamma and delta neutral.
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