Option-Implied Objective Measures of Market Risk

28 Pages Posted: 15 Nov 2015 Last revised: 19 Aug 2016

See all articles by Matthias Leiss

Matthias Leiss

ETH Zürich

Heinrich H. Nax

ETH Zürich; University of Zurich

Date Written: November 12, 2015

Abstract

Foster and Hart (2009) introduce an objective measure of the riskiness of an asset that implies a bound on how much of one’s wealth is ‘safe’ to invest in the asset while (a.s.) guaranteeing no-bankruptcy. In this study, we translate the Foster-Hart measure from static and abstract gambles to dynamic and applied finance using nonparametric estimation of risk-neutral densities from S&P 500 call and put option prices covering 2003 to 2013. The dynamics of the resulting ‘option-implied Foster-Hart bound’ are assessed in light of other well-known option-implied risk measures including value at risk, expected shortfall and risk-neutral volatility, as well as high moments of the densities and several industry measures. Rigorous variable selection reveals that the new measure is a significant predictor of (large) ahead-return downturns. Furthermore, it grasps more characteristics of the risk-neutral probability distributions in terms of moments than other measures and exhibits predictive consistency. The robustness of the risk-neutral density estimation is analyzed via Monte Carlo methods.

Keywords: risk measure, risk dynamics, risk-neutral densities, value at risk, expected shortfall

JEL Classification: D81, D84, G01, G32

Suggested Citation

Leiss, Matthias and Nax, Heinrich H., Option-Implied Objective Measures of Market Risk (November 12, 2015). Available at SSRN: https://ssrn.com/abstract=2690476 or http://dx.doi.org/10.2139/ssrn.2690476

Matthias Leiss (Contact Author)

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

Heinrich H. Nax

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006
Switzerland

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