Resource title

Spectral estimation of the fractional order of a Lévy process

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Resource description

We consider the problem of estimating the fractional order of a Lévy process from low frequency historical and options data. An estimation methodology is developed which allows us to treat both estimation and calibration problems in a unified way. The corresponding procedure consists of two steps: the estimation of a conditional characteristic function and the weighted least squares estimation of the fractional order in spectral domain. While the second step is identical for both calibration and estimation, the first one depends on the problem at hand. Minimax rates of convergence for the fractional order estimate are derived, the asymptotic normality is proved and a data-driven algorithm based on aggregation is proposed. The performance of the estimator in both estimation and calibration setups is illustrated by a simulation study.

Resource author

Denis Belomestny

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Resource publish date

Resource language

eng

Resource content type

text/html

Resource resource URL

http://hdl.handle.net/10419/25337

Resource license

Adapt according to the presented license agreement and reference the original author.