Realized Laplace Transforms for Estimation of Jump Diffusive Volatility Models

Todorov, Viktor; Tauchen, George; Grynkiv, Iaryna

doi:10.2139/ssrn.1687998

Cited by 11 publications

(15 citation statements)

References 54 publications

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“…There is strong evidence against the gamma or log-normal distribution, while the inverse Gaussian-implied by the class of nonGaussian Ornstein-Uhlenbeck processes of Barndorff-Nielsen and Shephard (2001) with tempered stable increments-has more support. These findings are consistent with Todorov, Tauchen, and Grynkiv (2011), but in disagreement with Corradi and Distaso (2006).…”

supporting

confidence: 66%

“…We also calculated these expressions based on the ARMA coefficients reported in the appendix of Todorov, Tauchen, and Grynkiv (2011), but the results differ and we suspect there are some typos in that paper.…”

Section: Resultsmentioning

confidence: 99%

“…To maintain a tractable setting, we proceed as in Todorov, Tauchen, and Grynkiv (2011). We assume the distribution of the increments of the volatility process corresponds to that of a tempered 22 Note.…”

Section: Empirical Applicationmentioning

confidence: 99%

“…Ornstein-Uhlenbeck process is discretized and simulated as explained in the appendix of Todorov, Tauchen, and Grynkiv (2011).…”

Section: Empirical Applicationmentioning

confidence: 99%

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The Realized Empirical Distribution Function of Stochastic Variance with Application to Goodness-of-Fit Testing

2018

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supporting

confidence: 66%

Section: Resultsmentioning

confidence: 99%

Section: Empirical Applicationmentioning

confidence: 99%

“…Ornstein-Uhlenbeck process is discretized and simulated as explained in the appendix of Todorov, Tauchen, and Grynkiv (2011).…”

Section: Empirical Applicationmentioning

confidence: 99%

See 2 more Smart Citations

The Realized Empirical Distribution Function of Stochastic Variance with Application to Goodness-of-Fit Testing

2018

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“…Following Barndorff-Nielsen and Shephard (2001), we specify the non-Gaussian OU process via its marginal distribution, which will be the inverse-Gaussian (which is self-decomposable and hence this is possible; e.g., see Sato 1999), with parameterization given in the previous subsection. It can be shown, for example, see Todorov, Tauchen, and Grynkiv (2011), that the Lévy measure of L t is given by…”

Section: Inverting Known Laplace Transformsmentioning

confidence: 99%

Inverse Realized Laplace Transforms for Nonparametric Volatility Density Estimation in Jump-Diffusions

Todorov

Tauchen

2012

Journal of the American Statistical Association

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This article develops a nonparametric estimator of the stochastic volatility density of a discretely observed Itô semimartingale in the setting of an increasing time span and finer mesh of the observation grid. There are two basic steps involved. The first step is aggregating the high-frequency increments into the realized Laplace transform, which is a robust nonparametric estimate of the underlying volatility Laplace transform. The second step is using a regularized kernel to invert the realized Laplace transform. These two steps are relatively quick and easy to compute, so the nonparametric estimator is practicable. The article also derives bounds for the mean squared error of the estimator. The regularity conditions are sufficiently general to cover empirically important cases such as level jumps and possible dependencies between volatility moves and either diffusive or jump moves in the semimartingale. The Monte Carlo analysis in this study indicates that the nonparametric estimator is reliable and reasonably accurate in realistic estimation contexts. An empirical application to 5-min data for three large-cap stocks, 1997-2010, reveals the importance of big short-term volatility spikes in generating high levels of stock price variability over and above those induced by price jumps. The application also shows how to trace out the dynamic response of the volatility density to both positive and negative jumps in the stock price.

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2012

Handbook of Volatility Models and Their Applications

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Realized Laplace Transforms for Estimation of Jump Diffusive Volatility Models

Cited by 11 publications

References 54 publications

The Realized Empirical Distribution Function of Stochastic Variance with Application to Goodness-of-Fit Testing

The Realized Empirical Distribution Function of Stochastic Variance with Application to Goodness-of-Fit Testing

Inverse Realized Laplace Transforms for Nonparametric Volatility Density Estimation in Jump-Diffusions

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