求解释

问题如下：

An option on the Bovespa stock index is struck on 3,000 Brazilian reais (BRL). The delta of the option is 0.6, and the annual volatility of the index is 24%. Using delta-normal assumptions, what is the 10-day VAR at the 95% confidence level? Assume 260 days per year.

选项：

A.

  44 BRL

B.

  139 BRL

C.

  2,240 BRL

D.

  278 BRL

解释：

ANSWER: B

The linear VAR is derived from the worst move in the index value, which is $\;\alpha S\sigma\sqrt T=1.645\times3000\times\frac{24\%}{\sqrt{260}}\times\sqrt{10}=232.3$. Multiplying by the delta of 0.6 gives 139.

解析：

现在有一个以股票index为基础资产的option价格为3000BRL，delta=0.6，年化σ=24%，用delta-normal的假设，求20天95%的VaR是多少？假设一年260天

95%置信区间对应的Z值=1.645

VaR=Z*S*delta*σ*区间调整

=1.645*3000*0.6*24%/(260^0.5)*(10^0.5)=139