Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets

69 Pages Posted: 4 Jun 2016 Last revised: 18 Jan 2021

See all articles by Chris Bardgett

Chris Bardgett

University of Zurich - Department Finance; École Polytechnique Fédérale de Lausanne

Elise Gourier

ESSEC Business School

Markus Leippold

University of Zurich; Swiss Finance Institute

Multiple version iconThere are 2 versions of this paper

Date Written: November 17, 2016


This paper shows that the VIX market contains information that is not already contained by the S&P 500 market on the variance of the S&P 500 returns. We estimate a flexible affine model based on a joint time series of underlying indexes and option prices on both markets. We find that including VIX option prices in the model estimation allows better identification of the parameters driving the risk-neutral conditional distributions and term structure of volatility, thereby enhancing the estimation of the variance risk premium. We gain new insights on the properties of the premium's term structure and show how they can be used to form trading signals. Finally, our premium has better predictive power than the usual model-free estimate and the higher-order moments of its term structure allow improving forecasts of S&P 500 returns.

Keywords: S&P 500 and VIX joint modeling, volatility dynamics, particle filter, variance risk premium

JEL Classification: G12, G13, C58

Suggested Citation

BARDGETT, Chris and Gourier, Elise and Leippold, Markus, Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets (November 17, 2016). Paris December 2016 Finance Meeting EUROFIDAI - AFFI, Available at SSRN: or


University of Zurich - Department Finance ( email )

Schönberggasse 1
Zürich, 8001

École Polytechnique Fédérale de Lausanne ( email )

c/o University of Geneve
40, Bd du Pont-d'Arve
1211 Geneva, CH-6900


Elise Gourier (Contact Author)

ESSEC Business School ( email )

3 avenue Bernard Hirsch
Cergy-Pontoise, 95021


Markus Leippold

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

Do you have negative results from your research you’d like to share?

Paper statistics

Abstract Views
PlumX Metrics