Bootstrapping Laplace Transforms of Volatility

42 Pages Posted: 3 Feb 2020 Last revised: 11 Aug 2022

See all articles by Ulrich Hounyo

Ulrich Hounyo

University at Albany, SUNY

Zhi Liu

University of Macau

Rasmus Tangsgaard Varneskov

Copenhagen Business School - Department of Finance; Nordea Bank AB - Nordea Asset Management

Date Written: January 21, 2020

Abstract

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.

Keywords: Bootstrap inference, Edgeworth expansions, High-frequency data, Higher-order refinements, Ito semimartingales, Realized Laplace transform, Spot measure inference

JEL Classification: C14, C15, C58, G1

Suggested Citation

Hounyo, Ulrich and Liu, Zhi and Varneskov, Rasmus Tangsgaard, Bootstrapping Laplace Transforms of Volatility (January 21, 2020). Available at SSRN: https://ssrn.com/abstract=3523293 or http://dx.doi.org/10.2139/ssrn.3523293

Ulrich Hounyo

University at Albany, SUNY ( email )

1400 Washington Avenue, Hudson Building, Suite 103
ALBANY, NY NY 12222
United States

Zhi Liu

University of Macau ( email )

E11-3072, University of Macau
Taipa, 999078
Macau

Rasmus Tangsgaard Varneskov (Contact Author)

Copenhagen Business School - Department of Finance ( email )

A4.17 Solbjerg Plads 3
Copenhagen, Frederiksberg 2000
Denmark

Nordea Bank AB - Nordea Asset Management ( email )

PO Box 850
Copenhagen, 0900
Denmark

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