Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-15T20:53:21.615Z Has data issue: false hasContentIssue false
  • English
  • Français

The Pricing of Volatility and Jump Risks in the Cross-Section of Index Option Returns

Published online by Cambridge University Press:  07 April 2022

Guanglian Hu Open the ORCID record for Guanglian Hu [Opens in a new window]  and
Yuguo Liu
Guanglian Hu*
Affiliation:
University of Sydney Discipline of Finance
Yuguo Liu
Affiliation:
University of Houston Department of Finance mailsforhugo@gmail.com
*
guanglian.hu@sydney.edu.au (corresponding author)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Existing studies relate the puzzling low average returns on out-of-the-money (OTM) index call and put options to nonstandard preferences. We argue the low option returns are primarily due to the pricing of market volatility risk. When volatility risk is priced, expected option returns match the realized average option returns. Moreover, consistent with its theoretical effect on expected option returns, the volatility risk premium is positively related to future index option returns and this relationship is stronger for OTM options and at-the-money straddles. Finally, we find the jump risk premium contributes to some portion of OTM put option returns.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 57 , Issue 6 , September 2022 , pp. 2385 - 2411
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of the Michael G. Foster School of Business, University of Washington

Footnotes

We thank Anandi Banerjee, David Bates (discussant), Jim Campasano (discussant), Jennifer Conrad (the editor), Christian Dorion, Hitesh Doshi, Bjorn Eraker, Neal Galpin, Quan Gan, Bing Han, Christopher Jones, Praveen Kumar, Gang Li (discussant), Hamish Malloch, Dmitriy Muravyev, Neil Pearson, Alessio Saretto (the referee), Sang Byung Seo, Longfei Shang (discussant), Aurelio Vasquez, and James Yae, seminar participants at the University of Houston, the University of Sydney, Monash University, the 2016 FMA PhD Student Session, the IFSID Fifth Conference on Derivatives, 2019 Derivative Markets Conference, 2019 FMA, 32nd Australasian Finance & Banking Conference, and Cancun Derivatives Workshop 2020, and especially Kris Jacobs for helpful comments.

References

Adrian, T., and Rosenberg, J.. “Stock Returns and Volatility: Pricing the Long-Run and Short-Run Components of Market Risk.” Journal of Finance, 63 (2008), 2997–3030.CrossRefGoogle Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Ebens, H.. “The Distribution of Realized Stock Return Volatility.” Journal of Financial Economics, 61 (2001), 43–76.Google Scholar
Andersen, T. G.; Bollerslev, T.; Diebold, F. X.; and Labys, P.. “Modeling and Forecasting Realized Volatility.” Econometrica, 71 (2003), 579–625.CrossRefGoogle Scholar
Andersen, T. G.; Fusari, N.; and Todorov, V.. “Parametric Inference and Dynamic State Recovery From Option Panels.” Econometrica, 83 (2015), 1081–1145.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), 259–299.CrossRefGoogle Scholar
Baele, L.; Driessen, J.; Ebert, S.; Londono, J. M.; and Spalt, O.. “Cumulative Prospect Theory, Option Returns, and the Variance Premium.” Review of Financial Studies, 32 (2019), 3667–3723.CrossRefGoogle Scholar
Bakshi, G.; Cao, C.; and Chen, Z.. “Empirical Performance of Alternative Option Pricing Model.” Journal of Finance, 52 (1997), 2003–2049.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.CrossRefGoogle Scholar
Bakshi, G.; Madan, D.; and Panayotov, G.. “Returns of Claims on the Upside and the Viability of U-Shaped Pricing Kernels.” Journal of Financial Economics, 97 (2010), 130–154.CrossRefGoogle Scholar
Barberis, N., and Huang, M.. “Stocks as Lotteries: The Implication of Probability Weighting for Security Prices.” American Economic Review, 98 (2008), 2066–2100.CrossRefGoogle Scholar
Barndorff-Nielsen, O. E., and Shephard, N.. “Econometric Analysis of Realised Volatility and Its Use in Estimating Stochastic Volatility Models.” Journal of the Royal Statistical Society, 64 (2002), 253–280.CrossRefGoogle Scholar
Bates, D. S. “The Crash of ’87: Was It Expected? The Evidence from Options Markets.” Journal of Finance, 46 (1991), 1009–1044.Google Scholar
Bates, D. S. “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutschemark Options.” Review of Financial Studies, 9 (1996), 69–107.Google Scholar
Bates, D. S. “Post-’87 Crash Fears in the S&P 500 Futures Option Market.” Journal of Econometrics, 94 (2000), 181–238.CrossRefGoogle Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–654.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
Bondarenko, O. “Why Are Put Options So Expensive?” Quarterly Journal of Finance, 4 (2014), 1450015.Google Scholar
Branger, N.; Hansis, A.; and Schlag, C.. “Expected Option Returns and the Structure of Jump Risk Premia.” Working Paper, University of Muenster (2010).Google Scholar
Broadie, M.; Chernov, M.; and Johannes, M.. “Model Specification and Risk Premia: Evidence from Futures Options.” Journal of Finance, 62 (2007), 1453–1490.CrossRefGoogle Scholar
Broadie, M.; Chernov, M.; and Johannes, M.. “Understanding Index Option Returns.” Review of Financial Studies, 22 (2009), 4493–4529.CrossRefGoogle Scholar
Brunnermeier, M. K.; Gollier, C.; and Parker, J. A.. “Optimal Beliefs, Asset Prices, and the Preference for Skewed Returns.” American Economic Review, 97 (2007), 159–165.Google Scholar
Cao, C., and Huang, J.-Z.. “Determinants of S&P 500 Index Option Returns.” Review of Derivatives Research, 10 (2007), 1–38.CrossRefGoogle Scholar
Carr, P., and Wu, L.. “Variance Risk Premiums.” Review of Financial Studies, 22 (2009), 1311–1341.CrossRefGoogle Scholar
Chambers, D. R.; Foy, M.; Liebner, J.; and Lu, Q.. “Index Option Returns: Still Puzzling.” Review of Financial Studies, 27 (2014), 1915–1928.CrossRefGoogle Scholar
Chaudhuri, R., and Schroder, M.. “Monotonicity of the Stochastic Discount Factor and Expected Option Returns.” Review of Financial Studies, 28 (2015), 1462–1505.CrossRefGoogle Scholar
Chernov, M., and Ghysels, E.. “A Study Towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Options Valuation.” Journal of Financial Economics, 56 (2000), 407–458.CrossRefGoogle Scholar
Christoffersen, P.; Heston, S.; and Jacobs, K.. “Capturing Option Anomalies with a Variance-Dependent Pricing Kernel.” Review of Financial Studies, 26 (2013), 1962–2006.Google Scholar
Cochrane, J. H., and Piazzesi, M.. “Bond Risk Premia.” American Economic Review, 95 (2005), 138–160.Google Scholar
Constantinides, G. M.; Czerwonko, M.; Jackwerth, J. C.; and Perrakis, S.. “Are Options on Index Futures Profitable for Risk-Averse Investors? Empirical Evidence.” Journal of Finance, 66 (2011), 1407–1437.Google Scholar
Constantinides, G. M., and Jackwerth, J. C.. “Mispricing of S&P 500 Index Options.” Review of Financial Studies, 22 (2009), 1247–1277.CrossRefGoogle Scholar
Constantinides, G. M.; Jackwerth, J. C.; and Savov, A.. “The Puzzle of Index Option Returns.” Review of Asset Pricing Studies, 3 (2013), 229–257.Google Scholar
Corsi, F. “A Simple Approximate Long-Memory Model of Realized Volatility.” Journal of Financial Econometrics, 7 (2009), 174–196.CrossRefGoogle Scholar
Coval, J. D., and Shumway, T.. “Expected Option Returns.” Journal of Finance, 56 (2001), 983–1009.CrossRefGoogle Scholar
Cremers, M.; Halling, M.; and Weinbaum, D.. “Aggregate Jump and Volatility Risk in the Cross-Section of Stock Returns.” Journal of Finance, 70 (2015), 577–614.CrossRefGoogle Scholar
Driessen, J., and Maenhout, P.. “An Empirical Portfolio Perspective on Option Pricing Anomalies.” Review of Finance, 11 (2007), 561–603.CrossRefGoogle Scholar
Driessen, J.; Maenhout, P. J.; and Vilkov, G.. “The Price of Correlation Risk: Evidence from Equity Options.” Journal of Finance, 64 (2009), 1377–1406.Google Scholar
Eraker, B. “Do Stock Prices And Volatility Jump? Reconciling Evidence From Spot And Option Prices.” Journal of Finance, 59 (2004), 1–37.CrossRefGoogle Scholar
Faias, J. A., and Santa-Clara, P.. “Optimal Option Portfolio Strategies: Deepening the Puzzle of Index Option Mispricing.” Journal of Financial and Quantitative Analysis, 52 (2017), 277–303.Google Scholar
Frazzini, A., and Pedersen, L. H.. “Embedded Leverage.” Working Paper, New York University (2012).Google Scholar
Gârleanu, N.; Pedersen, L. H.; and Poteshman, A. M.. “Demand-Based Option Pricing.” Review of Financial Studies, 22 (2009), 4259–4299.CrossRefGoogle 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), 327–343.Google Scholar
Israelov, R., and Kelly, B.. “Forecasting the Distribution of Option Returns.” Working Paper, University of Chicago (2017).Google Scholar
Jackwerth, J. C. “Recovering Risk Aversion from Option Prices and Realized Returns.” Review of Financial Studies, 13 (2000), 433–451.CrossRefGoogle Scholar
Johnson, T. L. “Risk Premia and the VIX Term Structure.” Journal of Financial and Quantitative Analysis, 52 (2017), 2461–2490.CrossRefGoogle Scholar
Jones, C. S. “The Dynamics of Stochastic Volatility: Evidence from Underlying and Options Markets.” Journal of Econometrics, 116 (2003), 181–224.CrossRefGoogle Scholar
Jones, C. S. “A Nonlinear Factor Analysis of S&P 500 Index Option Returns.” Journal of Finance, 61 (2006), 2325–2363.Google Scholar
Merton, R. C. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 4 (1973), 141–183.Google Scholar
Merton, R. C. “Option Pricing when Underlying Stock Returns are Discontinuous.” Journal of Financial Economics, 3 (1976), 125–144.Google Scholar
Mitton, T., and Vorkink, K.. “Equilibrium Underdiversification and the Preference for Skewness.” Review of Financial Studies, 20 (2007), 1255–1288.CrossRefGoogle Scholar
Muravyev, D., and Pearson, N. D.. “Options Trading Costs Are Lower Than You Think.” Review of Financial Studies, 33 (2020), 4973–5014.CrossRefGoogle Scholar
Naik, V., and Lee, M.. “General Equilibrium Pricing of Options on the Market Portfolio with Discontinuous Returns.” Review of Financial Studies, 3 (1990), 493–521.Google Scholar
Newey, W. K., and West, K. D.. “A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix.” Econometrica, 55 (1987), 703–727.Google Scholar
Newey, W. K., and West, K. D.. “Automatic Lag Selection in Covariance Matrix Estimation.” Review of Economic Studies, 61 (1994), 631–653.CrossRefGoogle 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.CrossRefGoogle Scholar
Polkovnichenko, V., and Zhao, F.. “Probability Weighting Functions Implied in Options Prices.” Journal of Financial Economics, 107 (2013), 580–609.Google Scholar
Rubinstein, M. “Implied Binomial Trees.” Journal of Finance, 49 (1994), 771–818.CrossRefGoogle Scholar
Santa-Clara, P., and Saretto, A.. “Option Strategies: Good Deals and Margin Calls.” Journal of Financial Markets, 12 (2009), 391–417.CrossRefGoogle Scholar
Todorov, V. “Variance Risk-Premium Dynamics: The Role of Jumps.” Review of Financial Studies, 23 (2010), 345–383.Google Scholar
Supplementary material: PDF

Hu and Liu supplementary material

Online Appendix

Download Hu and Liu supplementary material(PDF)
PDF 270.9 KB