Realized Laplace Transforms for Estimation of Jump Diffusive Volatility Models

We develop a new efficient and analytically tractable method for estimation of parametric volatility models that is robust to price-level jumps and generally has good finite sample properties. The method entails first integrating intra-day data into the Realized Laplace Transform of volatility, which is a model-free and jump-robust estimate of daily integrated empirical Laplace transform of the unobservable volatility. The estimation then is done by matching moments of the integrated joint Laplace transform with those implied by various parametric volatility models. In the empirical application, the best fitting volatility model is a non-diffusive two-factor model where low activity jumps drive its persistent component and more active jumps drive the transient one.