PhD Minor Oral: "Optimal iterative estimation of volatility using truncated realized variations"

Abstract: We consider a stochastic process driven by a diffusion and jump component, which are common in high frequency data in finance. Here, we are interested in estimating the integrated variance of the process, which is a global measure of riskiness of the asset during a fixed time interval. To filter out or mitigate the effect of the jump component, we use truncated realized quadratic variations with optimum thresholding, followed by a "fixed point'' iterative method for its implementation. The proposed iterative method starts with a data-driven initial guess of the true parameter of interest and then aims to iteratively improve this guess by using a formula for the optimal threshold that depends on the parameter of interest itself. The iterative estimator eventually settles down to some fixed value. We aim to fully characterize the asymptotic behavior of this final estimate, and prove the consistency and central limit results in the case of finite activity jumps under relatively mild assumptions. Furthermore, we consider a related iterative method under a stable L\'evy jump component.

Hosts: Jose Figueroa-Lopez and Brett Wick