Hostname: page-component-5d59c44645-mhl4m Total loading time: 0 Render date: 2024-02-26T11:51:07.768Z Has data issue: false hasContentIssue false

Risk Premia and the VIX Term Structure

Published online by Cambridge University Press:  27 December 2017


The shape of the Chicago Board Options Exchange Volatility Index (VIX) term structure conveys information about the price of variance risk rather than expected changes in the VIX, a rejection of the expectations hypothesis. The second principal component, SLOPE, summarizes nearly all this information, predicting the excess returns of synthetic Standard & Poor’s (S&P) 500 variance swaps, VIX futures, and S&P 500 straddles for all maturities and to the exclusion of the rest of the term structure. SLOPE’s predictability is incremental to other proxies for the conditional variance risk premia, economically significant, and inconsistent with standard asset pricing models.

Research Article
Copyright © Michael G. Foster School of Business, University of Washington 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



I thank Anat Admati, Mary Barth, Hendrik Bessembinder (the editor), Bjorn Eraker, Sebastian Infante, Bryan Kelly (the referee), Arthur Korteweg, Kristoffer Laursen, Ian Martin, Stefan Nagel, Paul Pfleiderer, Monika Piazzesi, Jan Schneider, Ken Singleton, Eric So, Suhas Sridharan, Mitch Towner, and seminar participants at Boston College, Dartmouth College, Rice University, Stanford University, University of California–Berkeley, University of Houston, University of Maryland, University of Pennsylvania, University of Rochester, University of Texas at Austin, and University of Wisconsin–Madison for their helpful comments. This paper is based on my dissertation at Stanford University titled “Essays on Information in Options Markets.”


Adrian, T., and Rosenberg, J.. “Stock Returns and Volatility: Pricing the Short-Run and Long-Run Components of Market Risk.” Journal of Finance, 63 (2008), 29973030.Google Scholar
Aıt-Sahalia, Y.; Karaman, M.; and Mancini, L.. “The Term Structure of Equity and Variance Risk Premia.” Working Paper, Princeton University (2015).Google Scholar
Ang, A.; Hodrick, R. J.; Xing, Y.; and Zhang, X.. “The Cross-Section of Volatility and Expected Returns.” Journal of Finance, 61 (2006), 259299.CrossRefGoogle Scholar
Bakshi, G., and Kapadia, N.. “Delta-Hedged Hains and the Negative Market Volatility Risk Premium.” Review of Financial Studies, 16 (2003), 527566.Google Scholar
Bakshi, G., and Madan, D.. “A Theory of Volatility Spreads.” Management Science, 52 (2006), 19451956.Google Scholar
Bakshi, G.; Panayotov, G.; and Skoulakis, G.. “Improving the Predictability of Real Economic Activity and Asset Returns with Forward Variances Inferred from Option Portfolios.” Journal of Financial Economics, 100 (2011), 475495.Google Scholar
Barras, L., and Malkhozov, A.. “Does Variance Risk Have Two Prices? Evidence from the Equity and Option Markets.” Journal of Financial Economics, 121 (2016), 7992.Google Scholar
Bekaert, G., and Hoerova, M.. “The VIX, the Variance Premium and Stock Market Volatility.” Journal of Econometrics, 183 (2014), 181192.Google Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637654.CrossRefGoogle Scholar
Bollerslev, T.; Tauchen, G.; and Zhou, H.. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22 (2009), 44634492.CrossRefGoogle Scholar
Breeden, D. T., and Litzenberger, R. H.. “Prices of State-Contingent Claims Implicit in Option Prices.” Journal of Business, 51 (1978), 621651.Google Scholar
Broadie, M.; Chernov, M.; and Johannes, M.. “Understanding Index Option Returns.” Review of Financial Studies, 22 (2009), 44934529.Google Scholar
Campbell, J. Y.; Giglio, S.; Polk, C.; and Turley, R.. “An Intertemporal CAPM with Stochastic Volatility.” Journal of Financial Economics, forthcoming (2017).Google Scholar
Carr, P., and Madan, D.. “Towards a Theory of Volatility Trading.” In Volatility, Vol. I, Jarrow, R., ed. Ann Arbor, MI: Risk Books (1998), 417427.Google Scholar
Carr, P., and Wu, L.. “Variance Risk Premiums.” Review of Financial Studies, 22 (2009), 13111341.Google Scholar
Christoffersen, P.; Heston, S.; and Jacobs, K.. “The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well.” Management Science, 55 (2009), 19141932.Google Scholar
Christoffersen, P.; Jacobs, K.; Ornthanalai, C.; and Wang, Y.. “Option Valuation with Long-Run and Short-Run Volatility Components.” Journal of Financial Economics, 90 (2008), 272297.Google Scholar
Cochrane, J. H., and Piazzesi, M.. “Bond Risk Premia.” American Economic Review, 95 (2005), 138160.Google Scholar
Corradi, V.; Distaso, W.; and Mele, A.. “Macroeconomic Determinants of Stock Volatility and Volatility Premiums.” Journal of Monetary Economics, 60 (2013), 203220.Google Scholar
Coval, J. D., and Shumway, T.. “Expected Option Returns.” Journal of Finance, 56 (2001), 9831009.CrossRefGoogle Scholar
Dew-Becker, I.; Giglio, S.; Le, A.; and Rodriguez, M.. “The Price of Variance Risk.” Journal of Financial Economics, 123 (2017), 225250.Google Scholar
Drechsler, I., and Yaron, A.. “What’s Vol Got to Do with It.” Review of Financial Studies, 24 (2011), 145.CrossRefGoogle Scholar
Egloff, D.; Leippold, M.; and Wu, L.. “The Term Structure of Variance Swap Rates and Optimal Variance Swap Investments.” Journal of Financial and Quantitative Analysis, 45 (2010), 12791310.Google Scholar
Eraker, B., and Wu, Y.. “Explaining the Negative Returns to VIX Futures and ETNs: An Equilibrium Approach.” Working Paper, University of Wisconsin (2014).Google Scholar
Feunou, B.; Fontaine, J.-S.; Taamouti, A.; and Tédongap, R.. “Risk Premium, Variance Premium, and the Maturity Structure of Uncertainty.” Review of Finance, 18 (2014), 219269.Google Scholar
Filipović, D.; Gourier, E.; and Mancini, L.. “Quadratic Variance Swap Models.” Journal of Financial Economics, 119 (2016), 4468.Google Scholar
Garleanu, N.; Pedersen, L. H.; and Poteshman, A. M.. “Demand-Based Option Pricing.” Review of Financial Studies, 22 (2009), 42594299.Google Scholar
Goyal, A., and Welch, I.. “A Comprehensive Look at the Empirical Performance of Equity Premium Prediction.” Review of Financial Studies, 21 (2008), 14551508.Google Scholar
Heston, S. L.A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” Review of Financial Studies, 6 (1993), 327343.Google Scholar
Hu, G. X.; Pan, J.; and Wang, J.. “Noise as Information for Illiquidity.” Journal of Finance, 68 (2013), 23412382.Google Scholar
Kozhan, R.; Neuberger, A.; and Schneider, P.. “The Skew Risk Premium in the Equity Index Market.” Review of Financial Studies, 26 (2013), 21742203.CrossRefGoogle Scholar
Martin, I.“Simple Variance Swaps.” Working Paper, London School of Economics (2013).Google Scholar
Mencía, J., and Sentana, E.. “Valuation of VIX Derivatives.” Journal of Financial Economics, 108 (2013), 367391.Google Scholar
Merton, R. C.An Intertemporal Capital Asset Pricing Model.” Econometrica, 41 (1973), 867887.Google Scholar
Mixon, S.The Implied Volatility Term Structure of Stock Index Options.” Journal of Empirical Finance, 14 (2007), 333354.Google Scholar
Neuberger, A.The Log Contract.” Journal of Portfolio Management, 20 (1994), 7480.Google Scholar
Newey, W. K., and West, K. D.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703708.Google Scholar
Todorov, V.Variance Risk-Premium Dynamics: The Role of Jumps.” Review of Financial Studies, 23 (2010), 345383.Google Scholar