Operator Methods for Measuring Systemic Risk Using High Frequency Options Panels

Abstract

Eigenfunction and quadrature methods have been extensively used in asset pricing to define forward looking pricing measures. In contrast, their use in generating systemic risk measures has been limited. Most uses of forward looking volatility models in systemic risk calculations have focused on using at-the-money Black-Scholes implied volatilities or eschewed derivatives based measures completely for parametric and semi-parametric models such as those from the GARCH family. With the advent of high frequency options panels we document a battery of measures that could be constructed and applied to the measurement of systemic risk, these include computationally intensive measures of cubic and quartic correlations. We outline the calculation of each measure and then present a useful library of statistical properties and stylized facts to allow macro-prudential policy makers to complement their existing risk measures.