Suppose that the current daily volatilities of asset X and asset Y are 1.0% and 1.2%, respectively. The prices of the assets at close of trading yesterday were $30 and $50 and the estimate of the coefficient of correlation between the returns on the two assets made at this time was 0.50. Correlations and volatilities are updated using a GARCH(1,1) model. The estimates of the model's parameters are α = 0:04 and β = 0:94. For the correlation α = 0:000001, and for the volatilities β = 0:000003.
If the prices of the two assets at close of trading today are $31 and $51, how is the correlation estimate updated?