Estimation of Volatility Functions in Jump Diffusions Using Truncated Bipower Increments

Résumé

In the paper, we introduce and analyze a new methodology to estimate the volatility functions of jump diffusion models. Our methodology relies on the standard kernel estimation technique using truncated bipower increments. The relevant asymptotics are fully developed, which allow for the time span to increase as well as the sampling interval to decrease and accommodate both stationary and nonstationary recurrent processes. We evaluate the performance of our estimators by simulation and provide some illustrative empirical analyses.

Mots-clés

nonparametric estimation; jump diffusion; aymptotics; diffusive and jump; volatility functions; Lévy measure; optimal bandwidth; bipower increment; threshold truncation;