  Volatility estimation based on high-frequency data is key to accurately
measure and control the risk of financial assets. A L\'{e}vy process with
infinite jump activity and microstructure noise is considered one of the
simplest, yet accurate enough, models for financial data at high-frequency.
Utilizing this model, we propose a "purposely misspecified" posterior of the
volatility obtained by ignoring the jump-component of the process. The
misspecified posterior is further corrected by a simple estimate of the
location shift and re-scaling of the log likelihood. Our main result
establishes a Bernstein-von Mises (BvM) theorem, which states that the proposed
adjusted posterior is asymptotically Gaussian, centered at a consistent
estimator, and with variance equal to the inverse of the Fisher information. In
the absence of microstructure noise, our approach can be extended to inferences
of the integrated variance of a general It\^o semimartingale. Simulations are
provided to demonstrate the accuracy of the resulting credible intervals, and
the frequentist properties of the approximate Bayesian inference based on the
adjusted posterior.
