Bootstrapping Laplace Transforms of Volatility

35 Pages Posted: 3 Feb 2020

See all articles by Ulrich Hounyo

Ulrich Hounyo

Aarhus University - CREATES

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 bootstraps provide inconsistent inference, we propose local Gaussian (LG) and modified wild (MW) bootstrap procedures, and establish their first-order asymptotic validity. Moreover, motivated by its superior finite sample performance in simulations, we use Edgeworth expansions to show that the LG inference achieves second-order asymptotic refinements. To further broaden the scope of the bootstraps, 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 inference procedures to the requisite scenario. We establish central limit theory for our estimators and show first-order asymptotic validity of their associated bootstraps. Not surprisingly, a Monte Carlo study shows that the LG bootstrap outperforms the MW bootstrap and existing (first-order) feasible inference theory in finite samples. Moreover, it demonstrates that our new spot measure estimators and inference procedures are very accurate. Finally, we illustrate the use of the new methods by examining the volatility of, and the coherence between, stocks and bonds during the large equity sell-off in December 2018.

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

Aarhus University - CREATES ( email )

School of Economics and Management
Building 1322, Bartholins Alle 10
DK-8000 Aarhus C
Denmark

Zhi Liu

University of Macau ( email )

P.O. Box 3001
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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