How does DCC-GARCH model time-varying correlation between assets?

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AcadiFi · Accepted Answer

Engle's Dynamic Conditional Correlation (DCC) GARCH decomposes the multivariate volatility problem in two stages. First, you fit a univariate GARCH to each series...

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The DCC(1,1) updating rule is Q_t = (1 - a - b) * Qbar + a * e_{t-1} e_{t-1}' + b * Q_{t-1}, where Qbar is the unconditional covariance of standardized residuals, and a, b are non-negative with a + b less than 1. The conditional correlation matrix is R_t = diag(Q_t)^{-1/2} Q_t diag(Q_t)^{-1/2}.

For Marlowe & Finch's pair book: suppose you're trading LMT vs NOC. Static correlation might be 0.62. During a defense-policy shock, DCC could jump conditional correlation to 0.89 over three weeks, then revert. This tells your execution desk to tighten hedge ratios dynamically.

Two caveats AcadiFi students should remember. First, the DCC model is often estimated in two steps, which loses some efficiency but makes high-dimensional fitting feasible. Second, Aielli (2013) pointed out a bias in the standard DCC estimator and proposed cDCC; for rigorous pair trading, cDCC is preferred. If you need asymmetric response to bad news, the ADCC extension adds a leverage term similar to GJR-GARCH.

How does DCC-GARCH model time-varying correlation between assets?

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