Question

Question

1.1 Suppose that the price of an asset at close of trading yesterday was $350 and its volatility was estimated as 1.4% per day. The price at the close of trading today is $347. Update the volatility estimate using

(a) The EWMA model with ʎ = 0.95,
(b) The GARCH(1,1) model with ω = 0.000003, α= 0.05, and β = 0.95

Answer 1

Price of a asset yesterday = $350

price today = $347

So, logarithmic return on the asset r_n-1 = ln(347/350) = -0.0086 or -0.86%

last day volatility σ_n-1 = 1.4%

a). So, using EWMA, current volatility is

σ²_n = (1-ʎ)*r²_n-1 + ʎ*σ²_n-1  = (1-0.95)*(0.0086^2) + 0.95*(0.014^2) = 0.0001899

So, volatility = 0.0001899^0.5 = 1.38%

b). Using GARCH(1,1), current volatility is

So, σ²_n = 0.000003 + 0.05*(0.0086^2) + 0.95*(0.014^2) = 0.0001929

=> Volatility = 0.0001929^0.5 = 1.39%

answered by: anonymous