一个投资组合包含1000股A股，和2000股B股。A和B的当前价格分别为83元和110元。假设A和B的对未来十天的百分比变化是正态分布，平均值（mean)是3％和2％，标准偏差(standard deviation）分别是5％和7％。A和B之间的相关性（correlation）是0.7。
a）计算10天的99％，投资组合的在险价值(VaR)。
b）假设我们添加一看涨期权（call option）到投资组合，其标的资产（underlying asset)爲1000万股A股,期权执行价格为85元，到期（maturity)是六个月。无风险利率为5％。计算投资组合的10天99％的在险价值(VaR)。



原文
A portfolio consists of 1,000 shares of A stock, and 2,000 of B stock. Current prices of A and B are $ 83 and $110  respectively. Suppose that the percentage changes of A and B for the next ten days are normally distributed, with means 3% and 2%, and standard deviations 5% and 7% respectively. Let the correlation between A and B be 0.7.

a) Calculate the ten-day 99% Value-at-Risk (VaR) of the portfolio.
b) Suppose further that we add to the portfolio a call option underlying 1,000 shares of A stock with strike price being $85, maturity being six months. Let the risk-free interest rate be 5%. Calculate the ten-day 99% VaR of the portfolio.



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