The Fourier estimator of volatility under coefficient explosions

Abstract In this paper, we study the Fourier estimator of volatility for a highly volatile asset price. To capture this situation, the price is modeled with an Itô semimartingale with coefficients that explode in finite time. This specification originated from the need to model abrupt movements of asset prices in tandem with abnormal drift/volatility behavior. We prove that the fundamental convolution formula of Malliavin and Mancino (Ann Stat 37(4):1983-2010, 2009) continues to hold true in this setting. We test the theory through numerical experiments with simulated data.