Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-09T03:18:14.688Z Has data issue: false hasContentIssue false
  • English
  • Français

Volatility-of-Volatility Risk

Published online by Cambridge University Press:  05 November 2018

Darien Huang Open the ORCID record for Darien Huang [Opens in a new window] ,
Christian Schlag ,
Ivan Shaliastovich  and
Julian Thimme
Get access Rights & Permissions [Opens in a new window]

Abstract

We show that market volatility of volatility is a significant risk factor that affects index and volatility index option returns, beyond volatility itself. The volatility and volatility of volatility indices, identified model-free as the VIX and VVIX, respectively, are only weakly related to each other. Delta-hedged index and VIX option returns are negative on average and are more negative for strategies that are more exposed to volatility and volatility-of-volatility risks. Further, volatility and volatility of volatility significantly negatively predict future delta-hedged option payoffs. The evidence suggests that volatility and volatility-of-volatility risks are jointly priced and have negative market prices of risk.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 54 , Issue 6 , December 2019 , pp. 2423 - 2452
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2018 

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.)

Footnotes

1

We thank an anonymous referee, Franklin Allen, Luca Benzoni, Hendrik Bessembinder (the editor), João Gomes, Mete Kilic, Krishna Ramaswamy, Scott Richard, Nikolai Roussanov, Anders Trolle, Amir Yaron, and Hao Zhou and seminar participants at the University of Pennsylvania, the 2014 European Finance Association Meeting, the 2014 OptionMetrics Research Conference, and the 2014 Asian Meeting of the Econometric Society for their comments and suggestions. Schlag gratefully acknowledges research and financial support from SAFE, funded by the State of Hessen initiative for research LOEWE. Shaliastovich thanks the Jacobs Levy Equity Management Center for Quantitative Financial Research, the Rodney White Center, and the Cynthia and Bennett Golub Endowment for financial support.

References

Bakshi, G.; Cao, C.; and Chen, Z.. “How Often Does the Call Move in the Opposite Direction to the Underlying? ” Review of Financial Studies, 13 (2000), 549–584.Google Scholar
Bakshi, G., and Kapadia, N.. “Delta-Hedged Gains and the Negative Market Volatility Risk Premium.” Review of Financial Studies, 16 (2003), 527–566.Google Scholar
Bakshi, G.; Kapadia, N.; and Madan, D.. “Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options.” Review of Financial Studies, 16 (2003), 101–143.Google Scholar
Bansal, R.; Kiku, D.; Shaliastovich, I.; and Yaron, A.. “Volatility, the Macroeconomy, and Asset Prices.” Journal of Finance, 69 (2014), 2471–2511.Google Scholar
Bansal, R., and Yaron, A.. “Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles.” Journal of Finance, 54 (2004), 1481–1509.Google Scholar
Barndorff-Nielsen, O., and Shephard, N.. “Power and Bipower Variation with Stochastic Volatility and Jumps.” Journal of Financial Econometrics, 2 (2004), 1–37.Google Scholar
Barndorff-Nielsen, O., and Shephard, N.. “Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation.” Journal of Financial Econometrics, 4 (2006), 1–30.Google Scholar
Bates, D.“Post-’87 Crash Fears in the S&P 500 Futures Option Market.” Journal of Econometrics, 94 (2000), 181–238.Google Scholar
Bertsimas, D.; Kogan, L.; and Lo, A.. “When Is Time Continuous? ” Journal of Financial Economics, 55 (2000), 173–204.Google Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–654.Google Scholar
Bloom, N.“The Impact of Uncertainty Shocks.” Econometrica, 77 (2009), 623–685.Google Scholar
Bollerslev, T.; Tauchen, G.; and Zhou, H.. “Expected Stock Returns and Variance Risk Premia.” Review of Financial Studies, 22 (2009), 4463–4492.Google Scholar
Branger, N.; Hülsbusch, H.; and Kraftschik, A.. “The Volatility-of-Volatility Term Structure.” Working Paper, University of Münster (2017).Google Scholar
Branger, N.; Kraftschik, A.; and Völkert, C.. “The Fine Structure of Variance: Pricing VIX Derivatives in Consistent and log-VIX Models.” Working Paper, University of Münster (2016).Google Scholar
Britten-Jones, M., and Neuberger, A.. “Option Prices, Implied Price Processes, and Stochastic Volatility.” Journal of Finance, 51 (2000), 621–651.Google Scholar
Campbell, J. Y.; Giglio, S.; Polk, C.; and Turley, R.. “An Intertemporal CAPM with Stochastic Volatility.” Journal of Financial Economics, 128 (2018), 207–233.Google Scholar
Canina, L., and Figlewski, S.. “The Informational Content of Implied Volatility.” Review of Financial Studies, 6 (1993), 659–681.Google Scholar
Cao, J., and Han, B.. “Cross-Section of Option Returns and Idiosyncratic Stock Volatility.” Journal of Financial Economics, 20 (2013), 1–10.Google Scholar
Carr, P., and Madan, D.. “Towards a Theory of Volatility Trading.” In Advances in Mathematical Finance, Cvitanic, J., Jouini, E., and Musiela, M., eds. Cambridge, UK: Cambridge University Press (1998).Google Scholar
Chen, Y.; Shu, J.; and Zhang, J. E.. “Investor Sentiment, Variance Risk Premium and Delta-Hedged Gains.” Applied Economics, 48 (2016), 2952–2964.Google Scholar
Christensen, B., and Prabhala, N.. “The Relation between Implied and Realized Volatility.” Journal of Financial Economics, 50 (1998), 125–150.Google Scholar
Christoffersen, P.; Jacobs, K.; and Mimouni, K.. “Volatility Dynamics for the S&P 500: Evidence from Realized Volatility, Daily Returns, and Option Prices.” Review of Financial Studies, 23 (2010), 3141–3189.Google Scholar
Coval, J., and Shumway, T.. “Expected Option Returns.” Journal of Finance, 56 (2001), 983–1009.Google Scholar
Cox, J.; Ingersoll, J.; and Ross, S.. “A Theory of the Term Structure of Interest Rates.” Econometrica, 53 (1985), 385–407.Google Scholar
Drechsler, I., and Yaron, A.. “What’s Vol Got to Do with It.” Review of Financial Studies, 24 (2010), 1–45.Google Scholar
Duarte, J., and Jones, C.. “The Price of Market Volatility Risk.” Working Paper, Rice University (2007).Google Scholar
Duffie, D.; Pan, J.; and Singleton, K.. “Transform Analysis and Asset Pricing for Affine Jump-Diffusions.” Econometrica, 68 (2000), 1343–1376.Google Scholar
Eraker, B.; Johannes, M.; and Polson, N.. “The Impact of Jumps in Returns and Volatility.” Journal of Finance, 53 (2003), 1269–1300.Google Scholar
Eraker, B., and Shaliastovich, I.. “An Equilibrium Guide to Designing Affine Pricing Models.” Mathematical Finance, 18 (2008), 519–543.Google Scholar
Fama, E., and MacBeth, J.. “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy, 81 (1973), 607–636.Google Scholar
Fernandez-Villaverde, J., and Rubio-Ramírez, J. F.. “Macroeconomics and Volatility: Data, Models, and Estimation.” In Advances in Economics and Econometrics: Theory and Applications, Acemoglu, D., Arellano, M., and Dekel, E., eds. Cambridge, UK: Cambridge University Press (2013).Google Scholar
Frazzini, A., and Pedersen, L.. “Embedded Leverage.” Working Paper, New York University (2012).Google Scholar
Heston, S.“A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bonds and Currency Options.” Review of Financial Studies, 6 (1993), 327–343.Google Scholar
Heston, S.; Korajczyk, R.; and Sadka, R.. “Intraday Patterns in the Cross-Section of Stock Returns.” Journal of Finance, 65 (2010), 1369–1407.Google Scholar
Hollstein, F., and Prokopczuk, M.. “How Aggregate Volatility-of-Volatility Affects Stock Returns.” Review of Asset Pricing Studies, 8 (2018), 253–292.Google Scholar
Huang, X., and Tauchen, G.. “The Relative Contribution of Jumps to Total Price Variation.” Journal of Financial Econometrics, 3 (2005), 456–499.Google Scholar
Hull, J. Options, Futures, and Other Derivatives. 8th ed. Upper Saddle River, NJ: Prentice Hall (2011).Google Scholar
Jiang, G., and Tian, Y.. “The Model-Free Implied Volatility and Its Information Content.” Review of Financial Studies, 18 (2005), 1305–1342.Google Scholar
Johnson, T.“Risk Premia and the VIX Term Structure.” Journal of Financial and Quantitative Analysis, 52 (2017), 2461–2490.Google Scholar
Liu, L.; Patton, A.; and Sheppard, K.. “Does Anything Beat 5-Minute RV? A Comparison of Realized Measures across Multiple Asset Classes.” Journal of Econometrics, 187 (2015), 293–311.Google Scholar
Lu, Z., and Zhu, Y.. “Volatility Components: The Term Structure Dynamics of VIX Futures.” Journal of Futures Markets, 30 (2010), 230–256.Google Scholar
Mencía, J., and Sentana, E.. “Valuation of VIX Derivatives.” Journal of Financial Economics, 108 (2013), 367–391.Google Scholar
Milstein, G. Numerical Integration of Stochastic Differential Equations. Boston, MA: Kluwer Academic (1995).Google Scholar
Muravyev, D.“Order Flow and Expected Option Returns.” Journal of Finance, 71 (2016), 673–708.Google Scholar
Pan, J.“The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study.” Journal of Financial Economics, 63 (2002), 3–50.Google Scholar
Park, Y.-H.“Volatility-of-Volatility and Tail Risk Hedging Returns.” Journal of Financial Markets, 26 (2015), 38–63.Google Scholar
Song, Z.“Expected VIX Option Returns.” Working Paper, Johns Hopkins University (2013).Google Scholar
Song, Z., and Xiu, D.. “A Tale of Two Option Markets: Pricing Kernels and Volatility Risk.” Journal of Econometrics, 190 (2016), 176–196.Google Scholar
Stein, J.“Overreactions in the Options Market.” Journal of Finance, 44 (1989), 1011–1023.Google Scholar
Tauchen, G., and Todorov, V.. “Volatility Jumps.” Journal of Business and Economic Statistics, 29 (2011), 235–371.Google Scholar
Wright, J., and Zhou, H.. “Bond Risk Premia and Realized Jump Risk.” Journal of Banking and Finance, 33 (2009), 2036–2049.Google Scholar
Zhang, J., and Zhu, Y.. “VIX Futures.” Journal of Futures Markets, 26 (2006), 521–531.Google Scholar
Supplementary material: File

Huang et al. supplementary material

Huang et al. supplementary material

Download Huang et al. supplementary material(File)
File 489.6 KB