arXiv 5 Jan 2024 · Econometrics
arXiv:2401.02819 · PDF · DOI · OpenAlex · Extracted main text
Inspired by the activity signature introduced by Todorov and Tauchen (2010), which was used to measure the activity of a semimartingale, this paper introduces the roughness signature function. The paper illustrates how it can be used to determine whether a discretely observed process is generated by a continuous process that is rougher than a Brownian motion, a pure-jump process, or a combination of the two. Further, if a continuous rough process is present, the function gives an estimate of the roughness index. This is done through an extensive simulation study, where we find that the roughness signature function works as expected on rough processes. We further derive some asymptotic properties of this new signature function. The function is applied empirically to three different volatility measures for the S&P500 index. The three measures are realized volatility, the VIX, and the option-extracted volatility estimator of Todorov (2019). The realized volatility and option-extracted volatility show signs of roughness, with the option-extracted volatility appearing smoother than the realized volatility, while the VIX appears to be driven by a continuous martingale with jumps.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Todorov, V (2019) Nonparametric spot volatility from options | 1.000 | 8 | 3 | 100% |
| 2 | Bennedsen, M (2020) Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data | 1.000 | 6 | 4 | 100% |
| 3 | Gatheral, J., T. Jaisson, and M. Rosenbaum (2018) Volatility is rough | 1.000 | 6 | 3 | 100% |
| 4 | Corcuera, J. M., E. Hedevang, M. S. Pakkanen, and M. Podolskij (2013) Asymptotic theory for brownian semi-stationary processes with application to turbulence | 0.977 | 15 | 5 | 93% |
| 5 | Todorov, V. and G. Tauchen (2010) Activity signature functions for high-frequency data analysis | 0.970 | 23 | 7 | 91% |
| 6 | Bolko, A. E., K. Christensen, M. S. Pakkanen, and B. Veliyev (2022) A gmm approach to estimate the roughness of stochastic volatility | 0.928 | 4 | 3 | 100% |
| 7 | Bennedsen, M., A. Lunde, and M. Pakkanen (2021) Decoupling the Short- and Long-Term Behavior of Stochastic Volatility | 0.928 | 4 | 3 | 100% |
| 8 | Bennedsen, M., K. Christensen, and P. Christensen (2023) Composite likelihood estimation of Gaussian moving average processes | 0.843 | 3 | 3 | 100% |
| 9 | Woerner, J (2011) Analyzing the Fine Structure of Continuous Time Stochastic Processes | 0.843 | 3 | 3 | 100% |
| 10 | Aït-Sahalia, Y. and J. Jacod (2009) Estimating the degree of activity of jumps in high frequency data | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 35 scored citations.