The Leverage Effect Puzzle under Semi-nonparametric Stochastic Volatility Models

Abstract

This article extends the solution proposed by Aït-Sahalia, Fan, and Li for the leverage effect puzzle, which refers to a fact that empirical correlation between daily asset returns and the changes of daily volatility estimated from high frequency data is nearly zero. Complementing the analysis in Aït-Sahalia, Fan, and Li via the Heston model, we work with a generic semi-nonparametric stochastic volatility model via an operator-based expansion method. Under such a general setup, we identify a new source of bias due to the flexibility of variance dynamics, distinguishing the leverage effect parameter from the instantaneous correlation parameter. For estimating the leverage effect parameter, we show that the main results on analyzing the various sources of biases as well as the resulting statistical procedures for biases correction in Aït-Sahalia, Fan, and Li hold true and are thus indeed theoretically robust. For estimating the instantaneous correlation parameter, we developed a new nonparametric estimation method.

Keywords:

• High-frequency data
• Leverage effect;Operator method
• Semi-nonparametric
• Stochastic volatility

Supplementary Materials

This supplementary material for The Leverage Effect Puzzle under Semi-nonparametric Stochastic Volatility Models contains (1) Proofs of Propositions 1–4, and Theorem 2 (Section S.1), (2) Extensions for incorporating market microstructure noise and/or jumps (Section S.2), (3) Additional simulation results for the case with market microstructure noise and jumps simultaneously (Section S.3), and (4) Proofs for the results in Section S.2 (Section S.4).

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

The research of Dachuan Chen is supported by the National Natural Science Foundation of China (grants 12101335 and 12271271), the Natural Science Foundation of Tianjin (grant 21JCQNJC00020), the Fundamental Research Funds for the Central Universities, Nankai University (grants 63211088 and 63221050) and the Wukong Investment Research Funds. The research of Chenxu Li was supported by the Guanghua School of Management, the Center for Statistical Science, the High-performance Computing Platform, and the Key Laboratory of Mathematical Economics and Quantitative Finance (Ministry of Education) at Peking University, as well as the National Natural Science Foundation of China (grant 72173003).