变量

NO.PZ2019040801000078

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：

5.429%.

3.241%.

3.009%.

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%

为什么current estimate of daily volatility 2.5%代表的是sigma(n-1)不是sigma(n)呢

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1 个答案

李坏_品职助教 · 2025年07月07日

嗨，努力学习的PZer你好：

根据EWMA的公式，目的是为了预测出左侧的波动率σn^2，说明在这个等式里面，n代表未来时刻。而等式右侧的σn-1 ^2代表的是前一天的波动率预测值。 μn-1代表前一天的return。

既然n代表未来（可以认为是明天），那么n-1自然代表今天的数据，所以current estimate of daily volatility对应的是σn-1

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努力的时光都是限量版，加油！

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