Suppose that the current daily volatilities of asset X and asset Y are 1.0% and 1.2%, respectively.

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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 ω = 0.000001 and for the volatilities ω = 0.000003. If the prices of the two assets at close of trading today are $31 and $51, how is the correlation estimate updated?

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