Strong rate for one-dimensional driftless continuous strict local martingales

For one-dimensional strict local martingales of the form $\mathrm{d} X_t=σ(X_t) \mathrm{d} W_t$ starting from $X_{0}=x_{0}>0$, we prove the strong rate $\mathbb{E}\left[|X^h_N-X_T|\right] \lesssim h^{\min\{θα,\frac{1}{2}\}}$ for a discrete scheme~$X^h$ truncated at a level $h^{-α}$, with time step~$