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Robust volatility estimation for multiscale diffusions with zero quadratic variation
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Manikas, Theodoros (2018) Robust volatility estimation for multiscale diffusions with zero quadratic variation. PhD thesis, University of Warwick.
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WRAP_Theses_Manikas_2018.pdf - Submitted Version - Requires a PDF viewer. Download (1115Kb) | Preview |
Official URL: http://webcat.warwick.ac.uk/record=b3253064~S1
Abstract
This thesis is concerned with the problem of volatility estimation in the context of multiscale diffusions. In particular, we consider data that exhibit two widely separated time scales. Fast/slow systems of SDEs that adopt a homogenized SDE are employed to model such data. The problem that one is confronted with, is the mismatch between the multiscale data and the homogenized SDE. In this context, we examine whether if by using the multiscale data, the diffusion coefficient of the homogenized SDE can be estimated. Our proposed estimator consists on subsampling the initial data by considering only the local extremals to overcome the issue associated with the underlying model. We provide both theoretical and numerical heuristics, suggesting that our proposed estimator when it is applied to multiscale data of bounded variation is asymptotically unbiased for the volatility coefficient of the homogenized SDE. Furthermore, for the particular example of a multiscale Ornstein-Uhlenbeck process, the numerical results indicate that the L₂-error of our estimator is very small. Moreover, we illustrate situations where the proposed estimator can also be used for multiscale data with bounded non-zero quadratic variation.
| Item Type: | Thesis or Dissertation (PhD) | ||||
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| Subjects: | Q Science > QA Mathematics | ||||
| Library of Congress Subject Headings (LCSH): | Diffusion processes, Parameter estimation, Stochastic differential equations, Multiscale modeling, Homogenization (Differential equations), Ornstein-Uhlenbeck process | ||||
| Official Date: | April 2018 | ||||
| Dates: |
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| Institution: | University of Warwick | ||||
| Theses Department: | Department of Statistics | ||||
| Thesis Type: | PhD | ||||
| Publication Status: | Unpublished | ||||
| Supervisor(s)/Advisor: | Papavasiliou, Anastasia, 1975- | ||||
| Sponsors: | University of Warwick. Department of Statistics | ||||
| Format of File: | |||||
| Extent: | x, 101 leaves : charts | ||||
| Language: | eng |
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