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Estimating time-changes in noisy L\'evy models

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  • Adam D. Bull

Abstract

In quantitative finance, we often model asset prices as a noisy Ito semimartingale. As this model is not identifiable, approximating by a time-changed Levy process can be useful for generative modelling. We give a new estimate of the normalised volatility or time change in this model, which obtains minimax convergence rates, and is unaffected by infinite-variation jumps. In the semimartingale model, our estimate remains accurate for the normalised volatility, obtaining convergence rates as good as any previously implied in the literature.

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  • Adam D. Bull, 2013. "Estimating time-changes in noisy L\'evy models," Papers 1312.5911, arXiv.org, revised Nov 2014.
    • Handle: RePEc:arx:papers:1312.5911
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    References listed on IDEAS

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    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    2. Fan, Jianqing & Wang, Yazhen, 2007. "Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1349-1362, December.
    3. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    4. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
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    Cited by:

    1. Belomestny, Denis & Schoenmakers, John, 2016. "Statistical inference for time-changed Lévy processes via Mellin transform approach," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2092-2122.
    2. Weiwei Guo & Lingfei Li, 2019. "Parametric inference for discretely observed subordinate diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 77-110, April.
    3. Todorov, Viktor, 2021. "Higher-order small time asymptotic expansion of Itô semimartingale characteristic function with application to estimation of leverage from options," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 671-705.
    4. Adam D. Bull, 2014. "Near-optimal estimation of jump activity in semimartingales," Papers 1409.8150, arXiv.org, revised Jan 2016.

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