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1\begin{table}[htbp]2\centering\small3\begin{threeparttable}4\caption{GARCH-family estimates for the ``No change'' contract (daily log returns, percent)}5\label{tab:garch}6\setlength{\tabcolsep}{4pt}7\begin{tabular}{l rrrr}8\toprule9 & GARCH & GJR-GARCH & GARCH & GJR-GARCH \\10Parameter & normal & normal & Student-$t$ & Student-$t$ \\11\midrule12 $\mu$ & 0.433 & 0.089 & 0.011 & -0.003 \\13 & (0.273) & (0.104) & (0.033) & (0.033) \\14 $\omega$ & 0.528 & 0.000 & 0.000 & 0.000 \\15 & (0.862) & (0.175) & (0.019) & (0.018) \\16 $\alpha_1$ & 0.183$^{**}$ & 0.000 & 0.291$^{**}$ & 0.000 \\17 & (0.083) & (0.890) & (0.141) & (0.055) \\18 $\gamma_1$ & -- & 0.304 & -- & 0.334$^{***}$ \\19 & & (0.721) & & (0.084) \\20 $\beta_1$ & 0.817$^{***}$ & 0.848 & 0.709$^{***}$ & 0.833$^{***}$ \\21 & (0.036) & (0.521) & (0.147) & (0.047) \\22 $\nu$ & -- & -- & 2.583$^{***}$ & 2.820$^{***}$ \\23 & & & (0.176) & (0.237) \\24\midrule25Log-likelihood & -461.2 & -425.3 & -382.4 & -373.6 \\26AIC & 930.4 & 860.6 & 774.8 & 759.1 \\27BIC & 942.3 & 875.5 & 789.6 & 777.0 \\28Persistence $\alpha_1+\beta_1+\gamma_1/2$ & 1.000 & 1.000 & 1.000 & 1.000 \\29Ljung--Box $p$, $z_t^2$ (10 lags) & 0.987 & 0.455 & 0.987 & 0.384 \\30Observations & \multicolumn{4}{c}{145} \\31\bottomrule32\end{tabular}33\begin{tablenotes}34\small35\item \textit{Notes:} Constant-mean models estimated by (quasi-)maximum likelihood on calendar-day log returns of the ``No change'' contract, listing day excluded; Bollerslev--Wooldridge robust standard errors in parentheses. The GJR variance equation is $\sigma_t^2=\omega+\alpha_1\varepsilon_{t-1}^2+\gamma_1\varepsilon_{t-1}^2\mathbf{1}\{\varepsilon_{t-1}<0\}+\beta_1\sigma_{t-1}^2$. The likelihood-ratio statistic for $\gamma_1=0$ (normal innovations) is 71.76 ($p=0.000$). Engle's ARCH-LM test (5 lags) on the returns: 4.92 ($p=0.426$). $^{***}$, $^{**}$, $^{*}$: 1\%, 5\%, 10\%.36\end{tablenotes}37\end{threeparttable}38\end{table}