Tim Bollerslev

Overview

Tim Bollerslev is an econometrician (Northwestern University, later Duke University) known for generalizing Engle's ARCH model to GARCH (1986) and for introducing the Constant Conditional Correlation (CCC) multivariate GARCH model (1990). His work with Engle and Wooldridge on the vech model (1988) and QML inference (1992) forms the methodological backbone of multivariate GARCH estimation.

Key Contributions

• GARCH (1986): Generalized ARCH by adding autoregressive variance terms — $\sigma_t^2 = \omega + \alpha\varepsilon_{t-1}^2 + \beta\sigma_{t-1}^2$; established the $\alpha+\beta<1$ covariance-stationarity condition and the IGARCH ($\alpha+\beta=1$) boundary case.
• vech model (BEW 1988): With Engle and Wooldridge, applied multivariate GARCH to the CAPM, demonstrating time-varying beta coefficients; QML robustness result.
• CCC (1990): $H_t = D_t\Gamma D_t$ with time-invariant $\Gamma$; concentrates $\Gamma$ out of the likelihood analytically; applied to five European currencies pre- and post-EMS inception.
• QML inference (1992): With Wooldridge, established the sandwich standard error formula for GARCH under non-normality.
• Answering the Skeptics (with Andersen 1998): Resolved the GARCH R² paradox. Low R² in squared-return regressions is a mathematical implication of correctly specified GARCH — the real problem is that squared daily returns are a very noisy proxy for latent variance (measurement noise ≈93% of regression residual for DM-$). Introduced realized volatility as the proper evaluation criterion; R² rises from ≈0.05 to ≈0.48 at 5-minute frequency, close to the theoretical maximum under the Nelson (1990) diffusion limit. See GARCH and BEKK-GARCH.
• Andersen-Bollerslev-Christoffersen-Diebold (2004): Co-authored practical risk management survey covering GARCH, DCC, realized variance, FHS, and critique of HS-VaR and RiskMetrics.
• Bollerslev-Zhou (2002): With Hao Zhou; Journal of Econometrics 109: 33–65. Estimated Heston SV diffusion using conditional moments of integrated volatility.
• Bollerslev-Zhou (2006): Three closed-form propositions under Heston (1993) explaining why realized-vol regressions produce negative feedback slopes, why implied vol shows stronger leverage asymmetry, and why implied vol forecasts are downward biased — all driven by $\rho < 0$ and $\lambda_v < 0$.

Related

• GARCH and BEKK-GARCH
• Stochastic Volatility
• Realized Volatility
• Quadratic Variation
• Andersen-Bollerslev-Diebold-Labys (2003)
• Paul Labys
• Risk-Return Tradeoff
• Robert Engle
• Torben G. Andersen
• Peter F. Christoffersen
• Francis X. Diebold
• Hao Zhou