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A financial institution has the following portfolio of over-the-counter options on GBP (sterling, UK currency): Type Position Delta of Option Gamma of Option Vega
A financial institution has the following portfolio of over-the-counter options on GBP (sterling, UK currency): 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 Call -500 -0.40 0.70 1.3 0.7 1.8 1.4 A traded option is available with a delta of 0.3, a gamma of 1.7, and a vega of 0.8. To make the portfolio both gamma-neutral and delta-neutral, you will take a (long/short) position in the traded option. You will also take a (long/short) position in GBP. How many GBP (i.e. don't worry about L/S, just write how many GBP)? Assume that all implied volatilities change by the same amount so that vegas can be aggregated. Enter your answer rounded to the nearest integer, skip the currency sign. For example, if your calculation results in GBP 9,876.1234567, you only need to enter 9876
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