Non-parametric estimation for some models driven by Levy processes Jose Enrique Figueroa Purdue University Abstract
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.
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