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玛卡巴卡123 · 2020年11月17日

问一道题：NO.PZ2019040801000078 [ FRM I ]

  1. FRM I
  2. Quantitative

问题如下：

Bridgewood uses an exponentially weighted moving average model (EWMA) to model the daily volatility of a stock. The decay factor is 0.85. The current estimate of daily volatility 2.5%. The stock closed at $35 yesterday and today's closing price is $33. Assume that we use continuously compounded returns. What is the updated estimate of volatility?

选项：

A.

5.429%.

B.

3.241%.

C.

3.009%.

D.

2.739%.

解释：

B is correct.

考点：Estimating Volatilities

解析：使用EWMA模型，Updated volatility estimate = [λ*(volatility_(t-1))^2 + (1-λ)*(current return)^2]^0.5

由题目条件，λ=0.85。而 Current return = ln(price today / price yesterday) =ln(33/35) = -5.884%

所以 Updated volatility estimate = [0.85*2.5%^2+0.15*(-5.884%)^2]^0.5 =3.241%

请问这里为什么不用算数回报率而要用ln回报率来计算呢？（股票收益率那部分
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1 个答案

袁园_品职助教 · 2020年11月18日

取对数有很多原因

一般 Continuously Compounded Return 用 ln

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NO.PZ2019040801000078问题如下Briewoouses exponentially weightemoving average mol (EWMto mol the ily volatility of a stock. The cfactor is 0.85. The current estimate of ily volatility 2.5%. The stoclose$35 yestery antoy's closing priis $33. Assume thwe use continuously compounreturns. Whis the upteestimate of volatility?A.5.429%.B.3.241%.C.3.009%.2.739%.B is correct.考点Estimating Volatilities解析使用EWMA模型，Uptevolatility estimate = [λ*(volatility_(t-1))^2 + (1-λ)*(current return)^2]^0.5由题目条件，λ=0.85。而 Current return = ln(pritoy / priyestery) =ln(33/35) = -5.884%所以 Uptevolatility estimate = [0.85*2.5%^2+0.15*(-5.884%)^2]^0.5 =3.241%current return 能否用33/35-1？一般题目中给什么关键词用ln？

2024-05-21 21:02 1 · 回答

NO.PZ2019040801000078 3.241%. 3.009%. 2.739%. B is correct. 考点Estimating Volatilities 解析使用EWMA模型，Uptevolatility estimate = [λ*(volatility_(t-1))^2 + (1-λ)*(current return)^2]^0.5 由题目条件，λ=0.85。而 Current return = ln(pritoy / priyestery) =ln(33/35) = -5.884% 所以 Uptevolatility estimate = [0.85*2.5%^2+0.15*(-5.884%)^2]^0.5 =3.241% 我计算的In（33/35）=3.555. 不知道是不是我的错

2022-02-04 10:22 1 · 回答

NO.PZ2019040801000078 3.241%. 3.009%. 2.739%. B is correct. 考点Estimating Volatilities 解析使用EWMA模型，Uptevolatility estimate = [λ*(volatility_(t-1))^2 + (1-λ)*(current return)^2]^0.5 由题目条件，λ=0.85。而 Current return = ln(pritoy / priyestery) =ln(33/35) = -5.884% 所以 Uptevolatility estimate = [0.85*2.5%^2+0.15*(-5.884%)^2]^0.5 =3.241%为什么最后这个公式开0.5的平方？这个公式在讲义哪里？

2021-04-07 00:16 1 · 回答