The Realized Laplace Transform of Volatility
提出一种基于高频数据的已实现拉普拉斯变换统计量，用于非参数估计潜在随机波动率的拉普拉斯变换，且对价格跳跃具有稳健性。
We introduce and derive the asymptotic behavior of a new measure constructed from high-frequency data which we call the realized Laplace transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long-span and infill asymptotics, the statistic can be used to construct a nonparametric estimate of the volatility Laplace transform as well as of the integrated joint Laplace transform of volatility over different points of time. We derive feasible functional limit theorems for our statistic both under fixed-span and infill asymptotics as well as under joint long-span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes.