  In this paper, we consider possibly misspecified stochastic differential
equation models driven by L\'{e}vy processes. Regardless of whether the driving
noise is Gaussian or not, Gaussian quasi-likelihood estimator can estimate
unknown parameters in the drift and scale coefficients. However, in the
misspecified case, the asymptotic distribution of the estimator varies by the
correction of the misspecification bias, and consistent estimators for the
asymptotic variance proposed in the correctly specified case may lose
theoretical validity. As one of its solutions, we propose a bootstrap method
for approximating the asymptotic distribution. We show that our bootstrap
method theoretically works in both correctly specified case and misspecified
case without assuming the precise distribution of the driving noise.
