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b. A financial institution has the following portfolio of over-the-counter options. Option Position Delta of Option W 120 0.9 X -80 1.2 Y 250 + (20 x Y) -0.8 Z -180 0.9 Gamma of Option 1.8 0.5 1.1 1.7 Vega of Option 1.5 0.4 0.9 1.2 Traded option A is available with a delta of 0.3, a gamma of 1.2, and a vega of 0.5. Traded option B is available with a delta of 0.6, a gamma of 1.8, and a vega of 0.9. What position in the traded options and in underlying stock would make the portfolio delta neutral, gamma neutral and vega neutral? (9 marks)

b. A financial institution has the following portfolio of over-the-counter options. Option Position Delta of Option W 120 0.9 X -80 1.2 Y 250 + (20 x Y) -0.8 Z -180 0.9 Gamma of Option 1.8 0.5 1.1 1.7 Vega of Option 1.5 0.4 0.9 1.2 Traded option A is available with a delta of 0.3, a gamma of 1.2, and a vega of 0.5. Traded option B is available with a delta of 0.6, a gamma of 1.8, and a vega of 0.9. What position in the traded options and in underlying stock would make the portfolio delta neutral, gamma neutral and vega neutral? (9 marks)

Essentials Of Investments
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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b. A financial institution has the following portfolio of over-the-counter options. Option Position Delta of Option W 120 0.9 X -80 1.2 Y 250 + (20 x Y) -0.8 Z -180 0.9 Gamma of Option 1.8 0.5 1.1 1.7 Vega of Option 1.5 0.4 0.9 1.2 Traded option A is available with a delta of 0.3, a gamma of 1.2, and a vega of 0.5. Traded option B is available with a delta of 0.6, a gamma of 1.8, and a vega of 0.9. What position in the traded options and in underlying stock would make the portfolio delta neutral, gamma neutral and vega neutral? (9 marks)
Transcribed Image Text:b. A financial institution has the following portfolio of over-the-counter options. Option Position Delta of Option W 120 0.9 X -80 1.2 Y 250 + (20 x Y) -0.8 Z -180 0.9 Gamma of Option 1.8 0.5 1.1 1.7 Vega of Option 1.5 0.4 0.9 1.2 Traded option A is available with a delta of 0.3, a gamma of 1.2, and a vega of 0.5. Traded option B is available with a delta of 0.6, a gamma of 1.8, and a vega of 0.9. What position in the traded options and in underlying stock would make the portfolio delta neutral, gamma neutral and vega neutral? (9 marks)
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