变化之后的Variance怎么求

问题如下：

Suppose that the price of asset X at the close of trading yesterday was USD 40 and its volatility was then estimated as 1.5% per day. Suppose further that the price of asset Y at the close of trading yesterday was USD 10 and its volatility was then estimated as 1.7%per day. The price of X and Y at the close of trading today are USD 38 and USD 10.1, respectively. The correlation between X and Y was estimated as 0.4 at the close of trading yesterday. Update the volatility of X and Y and the correlation between X and Y using the EWMA model with λ equal to 0.95.

解释：

The new estimates of the variance rate of X is

0.95 × 0.015^2 + 0.05 × (−2/40)^2 = 0.000339

which corresponds to a new volatility of 1.84%. The new volatility for Y is1.67%. The covariance yesterday was 0.015 × 0.017 × 0.4 = 0.000102. The new covariance is

0.95 × 0.000102 + 0.05 × (−2/40) × (0.1/10) = 0.0000719

The new correlation is 0.0000719/(0.0184 × 0.0167) = 0.23.

题目问：已知X资产昨日的收盘价是40，日波动率是1.5%。Y资产的昨日收盘价是10，日波动率是1.7%，X和Y今日收盘价是38和10.1，相关系数是0.4，λ是0.95，通过EMWA模型来计算一下新的X和Y的波动率以及correlation。

Xvolatility=[0.95 × 0.015^2 +0.05 × (−2/40)^2]^0.5=1.84%

Y volatility=1.76%

covariance=0.95 × 0.000102+ 0.05 × (−2/40) × (0.1/10) = 0.0000719

The new correlation is 0.0000719/(0.0184 × 0.0167) =0.23