Efficient estimation for the volatility of stochastic interest rate models

Yuping Song (), Hangyan Li and Yetong Fang
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Yuping Song: Shanghai Normal University
Hangyan Li: Shanghai Normal University
Yetong Fang: Renmin University of China

Statistical Papers, 2021, vol. 62, issue 4, No 15, 1939-1964

Abstract: Abstract The joint analysis of non-stationary and high frequency financial data poses theoretical challenges due to that such massive data varies with time and possesses no fixed density function. This paper proposes the local linear smoothing to estimate the unknown volatility function in scalar diffusion models based on Gamma asymmetric kernels for high frequency financial big data. Under the mild conditions, we obtain the asymptotic normality for the estimator at both interior and boundary design points. Besides the standard properties of the local linear estimator such as simple bias representation and boundary bias correction, the local linear smoothing using Gamma asymmetric kernels possesses some extra advantages such as variance reduction and resistance to sparse design, which is validated through finite sample simulation study and empirical analysis on 6-month Shanghai Interbank Offered Rate (abbreviated as Shibor) in China.

Keywords: Diffusion process; Volatility function; Local linear estimator; Gamma asymmetric kernel; Financial market interest rate; Primary 62G20; 62M05; Secondary 60J75; 62P20 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00362-020-01166-4

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