Estimating Volatility in Markets with Price Limits

Abstract

Daily price limits are popular in emerging financial markets. Estimating volatility in those markets faces difficulties. It is apparent that ignoring price limits or deleting prices on limit days will lead to underestimating the volatility. The degree of underestimation can be serious if price limits are rigid but the true volatility is not negligible. In this paper, we propose two methods: the renewal time method and the waiting time method. We prove the estimators of both methods are strongly consistent. We also compare the two methods through simulation and provide an illustration of the serious degree of underestimation resulting from either ignoring price limits or deleting prices on limit days.