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Estimation of the Continuous and Discontinuous Leverage Effects.

Yacine Aït-Sahalia1, Jianqing Fan2, Roger J A Laeven3

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Summary

This study reveals the presence of continuous and discontinuous leverage effects in asset returns, particularly highlighting the significance of the discontinuous component. Our statistical methods accurately estimate these effects, even with market microstructure noise.

Keywords:
Spot volatilityco-jumpshigh-frequency dataintegrated volatilityjumpsmarket microstructure noise

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Area of Science:

  • Quantitative Finance
  • Econometrics
  • Financial Market Analysis

Background:

  • The leverage effect, a negative correlation between asset returns and volatility changes, is a key feature in financial markets.
  • Existing models often assume continuous price and volatility processes, potentially overlooking important dynamics.

Purpose of the Study:

  • To investigate the leverage effect under a general framework allowing for Itô semimartingale processes for log-prices and volatility.
  • To develop and statistically validate methods for estimating continuous and discontinuous components of the leverage effect.
  • To extend these methods to account for market microstructure noise in observed returns.

Main Methods:

  • Decomposition of the leverage effect into continuous and discontinuous parts.
  • Development of statistical estimators for these components.
  • Establishment of asymptotic properties for the proposed estimators.
  • Extension of methods to handle noisy return data.
  • Monte Carlo simulations to assess finite sample performance.

Main Results:

  • The proposed statistical methods provide reliable estimation of both continuous and discontinuous leverage effects.
  • Empirical analysis of real financial data confirms the presence of both leverage effect components.
  • The discontinuous leverage effect is found to be particularly significant.

Conclusions:

  • The study provides robust statistical tools for analyzing the leverage effect in financial econometrics.
  • Empirical evidence strongly supports the existence of distinct continuous and discontinuous leverage effects.
  • The findings have implications for asset pricing, risk management, and market microstructure analysis.