Abstract
We construct a spot volatility kernel estimator of time-dependent diffusion models with jumps. Instead of idiomatic intraday return over an observation interval, in the proposed estimator, we use intraday range. Since the range represents the maximum difference among all observations within an interval, all data are used, and no information is lost. By setting a reasonable threshold and making the range not greater than it we effectively eliminate the negative effect of jump on volatility estimation. In this paper, we also prove the consistency and asymptotic normality of the estimator and testify its higher accuracy.
Highlights
In the analysis of financial markets, a correct description of the underlying variables is crucial
It is necessary to assume that the spot volatility is related to a specific state variable, and to time
Zu and Boswijk [2] constructed a spot volatility estimator for high-frequency data contaminated by market noise and presented a data-driven method to select the scale and bandwidth parameters
Summary
In the analysis of financial markets, a correct description of the underlying variables is crucial. Fan and Wang [1] used a kernel smoothing technique to consider spot volatility estimation for high-dimensional time-dependent diffusion models and proved the consistency and asymptotic normality of their proposed estimator. It is unconvincing to use the continuous diffusion models to describe high-frequency and even ultrahigh-frequency data Both theoretical and practical studies show that there are jumps in financial variables, which have important impacts in financial analysis (see Lee and Mykland [4] and Aït-Sahalia and Jacod [5]). Remark 3 By setting a reasonable threshold φ(δ) and controlling the range in a proper interval no more than the threshold, as δ → 0, the estimator βt can effectively eliminate the influence of jumps It is an ideal estimator of spot volatility in the jump diffusion models, which are more in line with the realities of financial markets
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