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irene · 2021年09月25日

new covariance

NO.PZ2020011303000087

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.

选项:

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.

请问考试new covariance的公式会考么?这个在考纲里么?上课似乎没讲吧

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品职答疑小助手雍 · 2021年09月26日

同学你好,这个公式讲义里没有直接讲,不过原版书36页里是有的。

covariance其实就是variance的一种变体,公式原理也和variance预测是一样的,95%乘以上一期的协方差,后面的0.05乘以新一期两个的变化率相乘。

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NO.PZ2020011303000087问题如下 Suppose ththe priof asset X the close of trang yestery wUS40 anits volatility wthen estimate1.5% per y. Suppose further ththe priof asset Y the close of trang yestery wUS10 anits volatility wthen estimate1.7%per y. The priof X anY the close of trang toy are US38 anUS10.1, respectively. The correlation between X anY westimate0.4 the close of trang yestery. Upte the volatility of X anY anthe correlation between X anY using the EWMA mol with λ equto 0.95. The new estimates of the varianrate of X is0.95 × 0.015^2 + 0.05 × (−2/40)^2 = 0.000339whicorrespon to a new volatility of 1.84%. The new volatility for Y is1.67%. The covarianyestery w0.015 × 0.017 × 0.4 = 0.000102. The new covarianis0.95 × 0.000102 + 0.05 × (−2/40) × (0.1/10) = 0.0000719The 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) = 0.0000719The new correlation is 0.0000719/(0.0184 × 0.0167) =0.23 可以讲一下变化之后的X,Y的volatility怎么算吗,老师讲过这个公式吗

2023-03-27 14:49 2 · 回答

NO.PZ2020011303000087 老师好,请问EWMA模型中的return不是对数收益率吗?应该用ln(pritoy/priyestery)来算的呀,这道题为什么直接用-2/40来算了?

2021-08-05 22:54 1 · 回答

请问new covariance的ewma 公式怎么出来的?

2020-04-02 16:50 1 · 回答