VaR置信区间单尾问题

问题如下：

A fund manager owns a portfolio of options on TUV, a non-dividend paying stock. 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, the volatility of TUV is 12% per year, and that each of the option and forward contracts is on one share of TUV, which of the following amounts would be closest to the 1-day 99% VaR of the portfolio?

选项：

A.USD 11,557 B.USD 12,627 C.USD 13,715 D.USD 32,000

解释：

C is correct. We need to map the portfolio to a position in the underlying stock TUV. A deep 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:

ꭤ = 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:

ꭤ*S*Dp*σ*sqrt(1/T) = (2.326)*(52)*(15,000)*(0.12/sqrt(252)) = USD 13,714.67