Non-parametric estimation for some models driven
by Levy processes
Jose Enrique Figueroa
Motivated by financial applications, continuous-time models driven by Levy processes have been proposed as natural alternatives to the traditional models driven by Brownian Motion. In light of the wide range of competing parametric models, non-parametric methods are crucial to lessen model biases in the estimation. In this talk, we propose and assess some non-parametric methods for Levy-based models under high-frequency, long horizon, sampling schemes. Two models considered here are tempered stable processes and time-changed Levy processes with instantaneous rate of time change determined by positive diffusions. The first model is semiparametric, encompassing several of the parametric models in the literature. Two of their appealing features are that their short-term increments are stable-like, while their long-term increments are normal-like. The random-clock in the second class aims at incorporating the intermittency, volatility clustering, and leverage phenomena exhibited by real financial data.