Realized volatility with stochastic sampling |
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Authors: | Masaaki Fukasawa |
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Institution: | Center for the Study of Finance and Insurance, Osaka University, 1-3 Machikaneyama-cho, Toyonaka, Osaka, 560-8531, Japan |
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Abstract: | A central limit theorem for the realized volatility of a one-dimensional continuous semimartingale based on a general stochastic sampling scheme is proved. The asymptotic distribution depends on the sampling scheme, which is written explicitly in terms of the asymptotic skewness and kurtosis of returns. Conditions for the central limit theorem to hold are examined for several concrete examples of schemes. Lower bounds for mean squared error and for asymptotic conditional variance are given, which are attained by using a specific sampling scheme. |
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Keywords: | High-frequency data Quadratic variation Stable convergence |
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