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xiaobaicp3 · 2025年02月28日

这题考的哪个公式

NO.PZ2024120401000080

问题如下:

Assume GARCH(1,1) parameters are given by:

σ2n = 0.000005 + 0.9σ2n-1 + 0.05u2n-1

Yesterday’s daily volatility was 2.0%. The asset price closed yesterday at $10.000 and was up to $11.052 today. What is the 10-day forward estimate of daily volatility?

选项:

A.

2.062%

B.

2.162%

C.

2.262%

D.

2.362%

解释:

long-run variance(VL) = 0.000005/(1-.95) = 0.0001,

last return(un-1) = Ln(11.052/10) = 10%,

current variance estimate(σ2n) = 0.000005 + 0.05*10%2 + 0.90*2%2 = 0.000865.

According to the equation of E[σ2n+t ]:

10-day forecast of variance = E[σ2n+10 ] = 1%2 + (0.05+0.9)10 *(0.000865 - 0.0001) = 0.000558.

So 10-day forecast of volatility = sqrt(0.000558) = 0.02362.

这题考的讲义中哪个公式呢

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