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A fund manager owns a portfolio of options on a non-dividend paying stock TUV. The portfolio is made up of 5,000 deep in-the-money call options on TUV and 20,000 deep out-of-the-money call options on TUV. The portfolio also contains 10,000 forward contracts on TUV. Currently, TUV is trading at USD 52. Assuming 252 trading days in a year and the volatility of TUV is 12% per year,
which of the following amounts would be closest to the 1-day VaR of the portfolio at the 99% confidence level？
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A) USD 11,557
B) USD 12,627
C) USD 13,715
D) USD 32,000
答案：C 》》》点击咨询FRM特惠课程
解析：We need to map the portfolio to a position in the underlying stock TUV.Adeep in-the-money call has a delta of approximately 1, a deep out-of-the-money call has a delta of approximately zero and forwards have a delta of 1. The net portfolio has a delta (Dp) of about 1*5,000 + 0*20,000 + 1*10,000 = 15,000 and is approximately gamma neutral. Let:
α = 2.326 (99% confidence level)
S = price per share of stock TUV = USD 52
Dp = delta of the position = 15,000
σ = volatility of TUV = 0.12
Therefore, the 1-day VaR estimate at 99% confidence level is computed as follows:
α×S×Δ×σ×sprt(1/T)=2.326×52×15,000×0.12×sprt(1∕252)=USD13,714.67
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