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A portfolio manager owns a portfolio of options on a non-dividend paying stock RTX. The portfolio is made up of 10,000 deep in-the-money call options on RTX and 50,000 deep out-of-the money call options on RTX. The portfolio also contains 20,000 forward contracts on RTX. RTX is trading at USD 100. If the volatility of RTX is 30% per year, which of the following amounts would be closest to the 1-day VaR of the portfolio at the 95 percent confidence level,
assuming 252 trading days in a year?
A) USD 932
B) USD 93,263
C) USD 111,122
D) USD 131,892
答案：B
解析：We need to map the portfolio to a position in the underlying stock RTX.Adeep in-the-money call has a delta of approximately 1, a deep out-of-the-money call has a delta of approximately 0 and forwards have a delta of 1. The net portfolio has a delta of about 30,000 and is approximately gamma neutral. The 1-day VaR estimate at 95 percent confidence level is computed as follows: a×S×△×σ×sqrt(1/T) = 1.645×100×30,000×0.30×sqrt(1/252) = 93,263
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