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Nonparametric range-based double smoothing spot volatility estimation for diffusion models. (English) Zbl 1451.62110

Summary: We consider nonparametric spot volatility estimation for diffusion models with discrete high frequency observations. Our estimator is carried out in two steps. First, using the local average of the range-based variance, we propose a crude estimator of the spot volatility. Second, we use usual nonparametric kernel smoothing to reconstruct the volatility function from the crude estimator. By inference, we find such a double smoothing operation can effectively reduce the estimation error.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62P20 Applications of statistics to economics
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