Double Smoothed Volatility Estimation of Potentially Non‐stationary Jump‐diffusion Model of Shibor

Abstract

The occurrence‐50 of economic policies and other sudden and large shocks often bring out jumps in financial data, which can be characterized through continuous‐time jump‐diffusion model. In this article, we present the double smoothed non‐parametric approach for infinitesimal conditional volatility of jump‐diffusion model based on high frequency data. Under certain minimal conditions, we obtain the strong consistency and asymptotic normality for the estimator as the time span T → ∞ and the sample interval normalΔn→0. The procedure and asymptotic behavior can be applied for both Harris recurrent and positive Harris recurrent processes. The finite sample properties of the underlying double smoothed volatility estimator are verified through Monte Carlo simulation and Shanghai Interbank Offered Rate in China for application.