The Realized Laplace Transform of Volatility

We introduce a new measure constructed from high-frequency financial data which we call the Realized Laplace Transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform of the latent stochastic volatility process over a given interval of time. When a long span of data is used, i.e., under joint long-span and fill-in asymptotics, it is an estimate of the volatility Laplace transform. The asymptotic behavior of the statistic depends on the small scale behavior of the driving martingale. We derive the asymptotics both in the case when the latter is known and when it needs to be inferred from the data. When the underlying process is a jump-diffusion our statistic is robust to jumps and when the process is pure-jump it is robust to presence of less active jumps. We apply our results to simulated and real financial data.