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王楚溪 · 2021年08月05日

EWMA模型里的return应该怎么计算

  1. FRM I
  2. Valuation And Risk Models

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.

老师好，请问EWMA模型中的return不是对数收益率吗？应该用ln(price today/price yesterday)来算的呀，这道题为什么直接用-2/40来算了？

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品职答疑小助手雍 · 2021年08月06日

嗨，爱思考的PZer你好：


没有说必须用对数收益率计算吧，讲义里的例题用的也是直接除的收益率的。

另外对于考试而言，除非涉及的题型直接让用对数收益率，否则对数收益和直接收益的误差基本是可以忽略的。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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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

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请问new covariance的ewma 公式怎么出来的?

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