10 天 99% VaR

正态近似下 VaR 近似满足

$$\operatorname{VaR}(N,C)\propto z_C\sqrt{N}.$$

因此

$$\boxed{\operatorname{VaR}(10,99\%)\approx \operatorname{VaR}(5,98\%)\cdot \frac{z_{0.99}\sqrt{10}}{z_{0.98}\sqrt{5}}}.$$

代入 $\operatorname{VaR}(5,98\%)=10\text{M}$，$z_{0.99}\approx 2.3263$，$z_{0.98}\approx 2.0537$，得到约 $16.0\text{M}$。

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英文解析

$$\operatorname{VaR}(N,C)\propto z_C\sqrt{N}.$$ $$\boxed{\operatorname{VaR}(10,99\%)\approx \operatorname{VaR}(5,98\%)\cdot \frac{z_{0.99}\sqrt{10}}{z_{0.98}\sqrt{5}}}.$$