Suppose stock price of Janus company at the close of trading yesterday was $10.00 and the most recent estimate of the daily volatility is 1.5%. The parameter λ in the EWMA (exponentially weighted moving average) model is 0.94. If the price at the close of trading today is $10.50, calculate the volatility to be updated by the EWMA model?

 

Assume FTSE 100 stock index at close of trading yesterday was 6,500 and the most recent estimate of the daily volatility of the index is 1.2%. The three parameters in a GARCH (1,1) model are ω = 0.000012,  α =  0.05, and β = 0.93. If the index at close of trading today is 6,620, calculate the daily volatility to be updated by the GARCH (1,1) model?

 

Suppose that the parameters in a GARCH (1,1) model are estimated from daily return data as ω  = 0.000013,  α =  0.04, and β = 0.91. What is the long-run average volatility per day implied by the model?

 

Assume that a risk manager uses maximum likelihood method to estimate the parameters of a GARCH(1,1) model. The risk manager initially chooses a random value for the parameter β, 0.89. This value increases to 0.91 after using Excel Solver tool, which gives the values for the parameters that maximize the likelihood of the data occurring. What is the impact of an increase of the parameter β  (from 0.89 to 0.91) on (1) the weight given to previous variance estimate, (2) weight to the long-run average variance rate, and (3) the level of the long-run average variance rate, respectively, while keeping the others fixed?