Event Details

Accounting and Finance, Finance seminar

Nicola Fusari, PhD (jhu.edu)

www.nicolafusari.com

Abstract

In this paper, we develop the first formal inference procedure for risk measures based on option

portfolios, such as the VIX. Specifically, for a panel of options with observation errors, we show that

the uncertainty about such measures depends critically on the spatial long-run variance (SLRV) of

the errors, that is, on their cross-sectional dependence across strikes. Hence, we propose a non-

parametric estimator of the SLRV that relies on spatial autocovariance estimates from second-order

cross-sectionally differenced observations to extract the parameters of an asymptotically increasing

moving average (MA) sequence. Importantly, to accommodate an increasing parameter space for

the MA approximation, we propose a new adaptive elastic net minimum distance estimator (AEN-

MDE) and establish its asymptotic properties in an infill asymptotic setting – the mesh of the strike

grid for the observed options shrinks asymptotically to zero, while the set of observation times and

tenors for the option panel remains fixed. Our novel inference theory, thus, bridges modern high-

dimensional methods with nonparametric long-run variance estimation and infill asymptotic limits.

A Monte Carlo study shows good finite-sample properties of the developed inference procedure,

and an empirical application to S&P 500 index option data reveals that the uncertainty about the

VIX and related indices has been declining in recent years.

Keywords: Heteroskedasticity, Infill Asymptotics, Large Data Sets, Nonparametric Estimation,

Option Portfolios, Spatial Dependence,