(b) A financial institution has the following portfolio of over-the-counter opti
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Question
(b) A financial institution has the following portfolio of over-the-counter options on sterling: Type Position Delta of Option Gamma of Option Vega of Option Call -1,000 0.5 2.2 1.8 Call -500 0.8 0.6 0.2 Put -2,000 -0.4 1.3 0.7 Call -500 0.7 1.8 1.4 A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8.
(i) What position in the traded option and in sterling would make the portfolio both gamma neutral and delta neutral?
(ii) What position in the traded option and in sterling would make the portfolio both vega neutral and delta neutral?
Explanation / Answer
Delta of the portfolio = -1,000 * 0.5 - 500 * 0.8 + 2,000 * 0.4 - 500 * 0.7
Delta of the portfolio = - 500 - 400 + 800 - 350
Delta of the portfolio = -450
Gamma of the portfolio = -1,000 * 2.2 - 500 * 0.6 - 2,000 * 1.3 - 500 * 1.8
Gamma of the portfolio = - 2,200 - 300 - 2,600 - 900
Gamma of the portfolio = -6,000
Vega of the portfolio = -1,000 * 1.8 - 500 * 0.2 - 2,000 * 0.7 - 500 * 1.4
Vega of the portfolio = - 1,800 - 100 - 1,400 - 700
Vega of the portfolio = -4,000
A long position in 4,000 traded options will give a gamma neutral portfolio since the long position has gamma of = 4,000 * 1.5 = 6,000
The delta of whole portfolio is = 4000 * 0.6 - 450 = 1,950
In addition to 4,000 traded options, a short position in 1,950 in sterrling is neccesary to make it both gamma and delta neutral
Part B
A long position in 5,000 traded options will give a vega neutral portfolio since the long position has vega of
= 5,000 * 0.8 = 4,000
The delta of whole portfolio is = 5000 * 0.6 - 450 = 2,550
In addition to 4,000 traded options, a short position in 2,550 in sterrling is neccesary to make it both vega and delta neutral
Type Position Delta of Option Gamma of Option Vega of Option Call -1,000 0.5 2.2 1.8 Call -500 0.8 0.6 0.2 Put -2,000 -0.4 1.3 0.7 Call -500 0.7 1.8 1.4Related Questions
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