Kim Christensen, Martin Thyrsgaard, Bezirgen Veliyev
arXiv 28 Jan 2026 · Econometrics
arXiv:2601.20469 · PDF · Extracted main text
We propose a nonparametric estimator of the empirical distribution function (EDF) of the latent spot variance of the log-price of a financial asset. We show that over a fixed time span our realized EDF (or REDF) -- inferred from noisy high-frequency data -- is consistent as the mesh of the observation grid goes to zero. In a double-asymptotic framework, with time also increasing to infinity, the REDF converges to the cumulative distribution function of volatility, if it exists. We exploit these results to construct some new goodness-of-fit tests for stochastic volatility models. In a Monte Carlo study, the REDF is found to be accurate over the entire support of volatility. This leads to goodness-of-fit tests that are both correctly sized and relatively powerful against common alternatives. In an empirical application, we recover the REDF from stock market high-frequency data. We inspect the goodness-of-fit of several two-parameter marginal distributions that are inherent in standard stochastic volatility models. The inverse Gaussian offers the best overall description of random equity variation, but the fit is less than perfect. This suggests an extra parameter (as available in, e.g., the generalized inverse Gaussian) is required to model stochastic variance.
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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 | S. L. Heston (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options | 1.000 | 7 | 3 | 100% |
| 2 | J. Li and V. Todorov and G. Tauchen (2016) Estimating the volatility occupation time via regularized Laplace inversion | 1.000 | 6 | 4 | 100% |
| 3 | V. Todorov and G. Tauchen and I. Grynkiv (2011) Realized Laplace transforms for estimation of jump diffusive volatility models | 1.000 | 6 | 4 | 100% |
| 4 | J. Jacod and Y. Li and P. A. Mykland and M. Podolskij and M. Vetter (2009) Microstructure noise in the continuous case: The pre-averaging approach | 1.000 | 6 | 3 | 100% |
| 5 | J. Li and V. Todorov and G. Tauchen (2013) Volatility occupation times | 0.969 | 11 | 6 | 91% |
| 6 | M. Podolskij and M. Vetter (2009) Bipower-type estimation in a noisy diffusion setting | 0.928 | 5 | 5 | 80% |
| 7 | O. E. Barndorff-Nielsen and N. Shephard (2001) Non-Gaussian Orstein-Uhlenbeck-based models and some of their uses in financial economics | 0.928 | 4 | 3 | 100% |
| 8 | V. Corradi and W. Distaso (2006) Semi-parametric comparison of stochastic volatility models using realized measures | 0.843 | 3 | 3 | 100% |
| 9 | V. Todorov and G. Tauchen (2012) The realized Laplace transform of volatility | 0.843 | 3 | 3 | 100% |
| 10 | A. W. van der Vaart (1998) Asymptotic Statistics | 0.737 | 4 | 2 | 75% |
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