Volatility estimation and jump detection for drift–diffusion processes

Sébastien Laurent*, Shuping Shi

*Corresponding author for this work

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The logarithmic prices of financial assets are conventionally assumed to follow a drift–diffusion process. While the drift term is typically ignored in the infill asymptotic theory and applications, the presence of temporary nonzero drifts is an undeniable fact. The finite sample theory for integrated variance estimators and extensive simulations provided in this paper reveal that the drift component has a nonnegligible impact on the estimation accuracy of volatility, which leads to a dramatic power loss for a class of jump identification procedures. We propose an alternative construction of volatility estimators and observe significant improvement in the estimation accuracy in the presence of nonnegligible drift. The analytical formulas of the finite sample bias of the realized variance, bipower variation, and their modified versions take simple and intuitive forms. The new jump tests, which are constructed from the modified volatility estimators, show satisfactory performance. As an illustration, we apply the new volatility estimators and jump tests, along with their original versions, to 21 years of 5-minute log returns of the NASDAQ stock price index.

Original languageEnglish
Pages (from-to)259-290
Number of pages32
JournalJournal of Econometrics
Volume217
Issue number2
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Diffusion process
  • Finite sample theory
  • Jumps
  • Nonzero drift
  • Volatility estimation

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