Realized Laplace transforms for estimation of jump diffusive volatility models

Todorov, Viktor; Tauchen, George; Grynkiv, Iaryna

doi:10.1016/j.jeconom.2011.06.016

Cited by 22 publications

(5 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The convergence rate of our new test under H 0 is of order n −1/2 when the jump component is of infinite variation, which is faster than that of all existing tests. The idea of the test is based on the realized characteristic function, which was introduced in Todorov and Tauchen (2012) to investigate the distributional property of volatilities at different time points; see also Todorov, Tauchen and Grynkiv (2011) and Jacod and Todorov (2014). With observable i.i.d.…”

mentioning

confidence: 99%

Testing for pure-jump processes for high-frequency data

Kong¹,

Li²,

Jing³

2015

Ann. Statist.

View full text Add to dashboard Cite

Pure-jump processes have been increasingly popular in modeling high-frequency financial data, partially due to their versatility and flexibility. In the meantime, several statistical tests have been proposed in the literature to check the validity of using pure-jump models. However, these tests suffer from several drawbacks, such as requiring rather stringent conditions and having slow rates of convergence. In this paper, we propose a different test to check whether the underlying process of high-frequency data can be modeled by a pure-jump process. The new test is based on the realized characteristic function, and enjoys a much faster convergence rate of order $O(n^{1/2})$ (where $n$ is the sample size) versus the usual $o(n^{1/4})$ available for existing tests; it is applicable much more generally than previous tests; for example, it is robust to jumps of infinite variation and flexible modeling of the diffusion component. Simulation studies justify our findings and the test is also applied to some real high-frequency financial data.Comment: Published at http://dx.doi.org/10.1214/14-AOS1298 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

show abstract

mentioning

confidence: 99%

Testing for pure-jump processes for high-frequency data

Kong¹,

Li²,

Jing³

2015

Ann. Statist.

View full text Add to dashboard Cite

show abstract

“…Specifically, they apply a similar nonlinear transformation of the SLT, which, however, is evaluated at a single u rather than integrated over a range,

u \in false[u_{normalmin}, u_{normalmax} false]

. Our design is motivated by the GMM inference procedure for stochastic volatility models in Todorov, Tauchen, and Grynkiv (2011), who integrate the realized Laplace transform over a range to harness most of its information. In particular, we leverage a similar idea in the context of the SLT to achieve robust estimation of the spot variance.…”

Section: Spot Laplace Transform and (Co)variance Inferencementioning

confidence: 99%

“…It captures the empirical Laplace transform of the spot variance process over a fixed interval of time, thus preserving information about the characteristics of volatility. Since its introduction by Todorov and Tauchen (2012b), the RLT has been utilized, among others, to design estimation procedures for stochastic volatility models, for example, Todorov, Tauchen, and Grynkiv (2011); volatility density estimation, Todorov and Tauchen (2012a); inference procedures and tests for the jump activity index, Todorov (2015); estimation of option pricing models, Andersen, Fusari, Todorov, and Varneskov (2019). These methods, however, generally use fixed‐span estimates of the RLT as ingredients in long‐span inference procedures (Andersen et al (2019) use a large option cross‐section), imposing stationarity and mixing‐type conditions on the volatility.…”

Section: Introductionmentioning

confidence: 99%

Bootstrapping Laplace transforms of volatility

Hounyo

Zhi

Varneskov

2023

View full text Add to dashboard Cite

This paper studies inference for the realized Laplace transform (RLT) of volatility in a fixed‐span setting using bootstrap methods. Specifically, since standard wild bootstrap procedures deliver inconsistent inference, we propose a local Gaussian (LG) bootstrap, establish its first‐order asymptotic validity, and use Edgeworth expansions to show that the LG bootstrap inference achieves second‐order asymptotic refinements. Moreover, we provide new Laplace transform‐based estimators of the spot variance as well as the covariance, correlation, and beta between two semimartingales, and adapt our bootstrap procedure to the requisite scenario. We establish central limit theory for our estimators and first‐order asymptotic validity of their associated bootstrap methods. Simulations demonstrate that the LG bootstrap outperforms existing feasible inference theory and wild bootstrap procedures in finite samples. Finally, we illustrate the use of the new methods by examining the coherence between stocks and bonds during the global financial crisis of 2008 as well as the COVID‐19 pandemic stock sell‐off during 2020, and by a forecasting exercise.

show abstract

“…Matching moments of the latter with that implied by a model provides for an efficient, robust, and often analytically convenient model determination and estimation of the volatility dynamics. This latter effort is far beyond the scope of this paper and is undertaken in a follow-up paper (Todorov, Tauchen, and Grynkiv (2011)) that applies the limit theory developed here.…”

Section: Introductionmentioning

confidence: 99%

The Realized Laplace Transform of Volatility

2012

Econometrica

View full text Add to dashboard Cite

We introduce and derive the asymptotic behavior of a new measure constructed from high‐frequency data which we call the realized Laplace transform of volatility. The statistic provides a nonparametric estimate for the empirical Laplace transform function of the latent stochastic volatility process over a given interval of time and is robust to the presence of jumps in the price process. With a long span of data, that is, under joint long‐span and infill asymptotics, the statistic can be used to construct a nonparametric estimate of the volatility Laplace transform as well as of the integrated joint Laplace transform of volatility over different points of time. We derive feasible functional limit theorems for our statistic both under fixed‐span and infill asymptotics as well as under joint long‐span and infill asymptotics which allow us to quantify the precision in estimation under both sampling schemes.

show abstract

Realized Laplace transforms for estimation of jump diffusive volatility models

Cited by 22 publications

References 51 publications

Testing for pure-jump processes for high-frequency data

Testing for pure-jump processes for high-frequency data

Bootstrapping Laplace transforms of volatility

The Realized Laplace Transform of Volatility

Contact Info

Product

Resources

About