Variance reduction approach for the volatility over a finite-time horizon

Abstract

The volatility is a measure for the uncertainty of an asset’s return and is used to reflect the risk level of a financial asset. In this article, we consider the double kernel nonparametric estimator for the volatility function in a diffusion model over a finite-time span based on high frequency sampling data. Under the minimum conditions, the asymptotic mixed normality for the underlying estimator is derived. Moreover, the better finite-sample performance as variance reduction and even mean squared error reduction of the proposed estimator is verified through a Monte Carlo simulation study and an empirical analysis on overnight Shibor in China.

Keywords:

• Diffusion process
• volatility function
• double kernel estimator
• short-term interest rate
• high frequency data

MSC 2010: Primary:

• 62G20
• 62M05
• Secondary 60J75
• 62P20

JEL CLASSIFICATION:

• C13
• C14
• C22

Data availability statement

The dataset for the empirical analysis is available as a supplementary file, which can also be derived from the following resource available in the public domain: http://www.shibor.org/shibor/web/DataService.jsp.

Additional information

Funding

Song’s research work is supported by National Natural Science Foundation of China (11901397), Ministry of Education, Humanities and Social Sciences project (18YJCZH153), National Statistical Science Research Project (2018LZ05), Youth Academic Backbone Cultivation Project of Shanghai Normal University (310-AC7031-19-003021), General Research Fund of Shanghai Normal University (SK201720) and Key Subject of Quantitative Economics (310-AC7031-19-004221) and Academic Innovation Team (310-AC7031-19-004228) of Shanghai Normal University. Chen’s research work is supported by Natural Science Foundation of Zhejiang Province (Grant No. LQ18A010009).