Bias reduction in spot volatility estimation from options

We consider the problem of nonparametric spot volatility estimation from options that is robust to time-variation in volatility and presence of jumps in the underlying asset price. Using a higher-order expansion of the characteristic function of the underlying price increment over shrinking time intervals and option-based estimates of the latter over two distinct horizons, we achieve asymptotic bias-reduction in spot volatility estimation, relative to existing methods, that is due to time-variation in volatility and presence of jumps. Further asymptotic improvement is achieved by de-biasing the volatility estimator using an estimate for the bias in it due to the small jumps in the price process. The gains from the newly-developed volatility estimation approach are illustrated on simulated data and in an empirical application.