题目
A financial institution has the following portfolio of over-the-counter options on sterling A traded option is available with a delta of 0.6, a gamma of 1.5, a vega of 0.8.What position in the traded option and in sterling would make the portfolio both gamma neutral and delta neutral?
选项
A.Short position in 4000 traded options, long position in 1950 sterling.
B.Long position in 4000 traded options, short position in 1950 sterling.
C.Long position in 4000 traded options, long position in 1950 sterling.
D.Short position in 4000 traded options, short position in 1950 sterling.
答案
B
解析
The delta of the portfolio:-1,000×0.50-500×0.80-2,000×(-0.40)-500×0.70=-450The gamma of the portfolio:-1,000×2.2-500×0.6-2,000×1.3-500×1.8=-6000The vega of the portfolio:-1,000×1.8-500×0.2-2,000×0.7-500×1.4=-4000A long position in 4,000 traded options will give a gamma-neutral portfolio since the long position has a gamma of 4,000×1.5=+6,000. The delta of the whole portfolio (including traded options) is then: 4,000×0.6-450=1,950.Hence, in addition to the 4,000 traded options, a short position in 1,950 is necessary so that the portfolio is both gamma and delta neutral.投资组合的delta为：－1,000×0.50－500×0.80－2,000×(－0.40)－500×0.70=－450投资组合的gamma为：－1,000×2.2－500×0.6－2,000×1.3－500×1.8=－6000投资组合的vega为：－1,000×1.8－500×0.2－2,000×0.7－500×1.4=?4000多头4,000个交易期权的多头头寸将提供gamma中性投资组合，因为多头头寸的gamma为4, 000×1.5= 6, 000。然后，珍格格投资组合的delta为4,000×0.6?450=1, 950因此，除了4,000个交易期权外，还需要在1,950个空头头寸，以便该投资组合既是gamma中性又是delta中性。