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