Hostname: page-component-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-06-24T05:34:33.317Z Has data issue: false hasContentIssue false
  • English
  • Français

Heterogeneity in Beliefs and Volatility Tail Behavior

Published online by Cambridge University Press:  24 February 2016

Gurdip Bakshi ,
Dilip Madan  and
George Panayotov
Gurdip Bakshi*
Affiliation:
gbakshi@rhsmith.umd.edu, University of Maryland, Smith School of Business, College Park, MD 20742
Dilip Madan
Affiliation:
dbm@rhsmith.umd.edu, University of Maryland, Smith School of Business, College Park, MD 20742
George Panayotov
Affiliation:
panayotov@ust.hk, Hong Kong University of Science and Technology, School of Business, Clearwater Bay, Hong Kong.
*
*Corresponding author: gbakshi@rhsmith.umd.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

We propose a model of volatility tail behavior in which investors display aversion to both low-volatility and high-volatility states, and hence, the derived pricing kernel exhibits an increasing and decreasing region in the volatility dimension. The model features investors who have heterogeneity in beliefs about volatility outcomes and maximize their utility by choosing volatility-contingent cash flows. Our empirical examination suggests that the model is better suited to reproduce data features in the left tail of the volatility distribution, both qualitatively and quantitatively.

Type
Research Articles
Information
Journal of Financial and Quantitative Analysis , Volume 50 , Issue 6 , December 2015 , pp. 1389 - 1414
Copyright
Copyright © Michael G. Foster School of Business, University of Washington 2016 

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.)

References

Aït-Sahalia, Y.; Karaman, M.; and Mancini, L.. “The Term Structure of Variance Swaps and Risk Premia.” Working Paper, Princeton University (2013).Google Scholar
Aït-Sahalia, Y., and Lo, A.. “Nonparametric Risk Management and Implied Risk Aversion.” Journal of Econometrics, 94 (2000), 9–51.Google Scholar
Aït-Sahalia, Y., and Mancini, L.. “Out of Sample Forecasts of Quadratic Variation.” Journal of Econometrics, 147 (2008), 17–33.CrossRefGoogle Scholar
Amengual, D., and Xiu, D.. “Resolution of Policy Uncertainty and Sudden Declines in Volatility.” Working Paper, University of Chicago (2013).Google Scholar
Andersen, T.; Bollerslev, T.; Diebold, F.; and Labys, P.. “Modeling and Forecasting Realized Volatility.” Econometrica, 71 (2003), 529–626.Google Scholar
Andersen, T.; Bollerslev, T.; and Meddahi, N.. “Correcting the Errors: Volatility Forecast Evaluation Using High-Frequency Data and Realized Volatilities.” Econometrica, 73 (2005), 279–296.Google Scholar
Bagnoli, M., and Bergstrom, T.. “Log-Concave Probability and its Applications.” Economic Theory, 26 (2005), 445–469.Google 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.Google Scholar
Basak, S. “A Model of Dynamic Equilibrium Asset Pricing with Heterogeneous Beliefs and Extraneous Risk.” Journal of Economic Dynamics and Control, 24 (2000), 63–95.CrossRefGoogle Scholar
Basak, S. “Asset Pricing with Heterogeneous Beliefs.” Journal of Banking and Finance, 29 (2005), 2849–2881.Google Scholar
Black, F. “Studies of Stock Price Volatility Changes.” In Proceedings of the 1976 American Statistical Association, Business and Economical Statistics Section, Alexandria, VA: American Statistical Association (1976), 177–181.Google Scholar
Bollerslev, T., and Todorov, V.. “Tails, Fears, and Risk Premia.” Journal of Finance, 66 (2011), 2165–2211.Google Scholar
Brennan, M. “The Pricing of Contingent Claims in Discrete Time Models.” Journal of Finance, 34 (1979), 53–68.Google Scholar
Briys, E.; Crouhy, M.; andSchlesinger, H.. “Optimal Hedging under Intertemporally Dependent Preferences.” Journal of Finance, 45 (1990), 1315–1324.CrossRefGoogle Scholar
Buehler, H. “Consistent Variance Curve Models.” Finance and Stochastics, 10 (2006), 178–203.Google Scholar
Buraschi, A., and Jiltsov, A.. “Model Uncertainty and Option Markets with Heterogeneous Beliefs.” Journal of Finance, 61 (2006), 2841–2897.Google Scholar
Calvet, L.; Grandmont, J.-M.; and Lemaire, I.. “Aggregation of Heterogeneous Beliefs, Asset Pricing and Risk Sharing in Complete Markets.” Working Paper, HEC Paris, and CREST (2004).Google Scholar
Carr, P., and Lee, R.. “Robust Replication of Volatility Derivatives.” Working Paper, New YorkUniversity and University of Chicago 2008.Google Scholar
Carr, P., and Wu, L.. “Variance Risk Premia.” Review of Financial Studies, 22 (2009), 1311–1341.Google Scholar
Chen, H.; Joslin, S.; and Tran, N.-K.. “Rare Disasters and Risk Sharing with Heterogeneous Beliefs.” Review of Financial Studies, 25 (2012), 2189–2224.Google Scholar
Chicago Board Options Exchange. “VIX: Fact & Fiction.” Working Paper, Chicago Board Options Exchange (2009).Google Scholar
Christoffersen, P.; Heston, S.; and Jacobs, K.. “Capturing Option Anomalies with a Variance-Dependent Pricing Kernel.” Review of Financial Studies, 26 (2013), 1963–2006.CrossRefGoogle Scholar
Cont, R., and Kokholm, T.. “A Consistent Pricing Model for Index Options and Volatility Derivatives.” Mathematical Finance, 23 (2013), 248–274.Google Scholar
Coval, J., and Shumway, T.. “Expected Option Returns.” Journal of Finance, 56 (2001), 983–1009.Google Scholar
Cox, J. C., and Huang, C.. “Optimal Consumption and Portfolio Policies When Asset Prices Follow a Diffusion Process.” Journal of Economic Theory, 49 (1989), 33–83.Google Scholar
DeGroot, M., and Schervish, M.. Probability and Statistics. New York, NY: Addison Wesley (2002).Google Scholar
Detemple, J., and Murthy, S.. “Intertemporal Asset Pricing with Heterogeneous Beliefs.” Journal of Economic Theory, 62 (1994), 294–320.Google Scholar
Dieckmann, S. “Rare Event Risk and Heterogeneous Beliefs: The Case of Incomplete Markets.” Journal of Financial and Quantitative Analysis, 46 (2011), 459–488.Google 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), 1279–1310.Google Scholar
Föllmer, H., and Schied, A.. Stochastic Finance: An Introduction in Discrete Time. Berlin, Germany: Walter de Gruyer (2004).Google Scholar
Gatheral, J. “Consistent Modeling of SPX and VIX Options.” In The Fifth World Congress of the Bachelier Finance Society. London, UK: Wiley 2008.Google Scholar
Grossman, S., and Stiglitz, J.. “On the Impossibility of Informationally Efficient Markets.” American Economic Review, 70 (1980), 393–408.Google Scholar
Hansen, L., and Jagannathan, R.. “Implications of Security Market Data for Dynamic Economies.” Journal of Political Economy, 99 (1991), 225–261.Google Scholar
Hong, H. “A Model of Returns and Trading in Futures Markets.” Journal of Finance, 55 (2000), 959–988.Google Scholar
Huang, C., and Litzenberger, R.. Foundations for Financial Economics. Upper Saddle River, NJ: Prentice Hall 1988.Google Scholar
Jackwerth, J., and Vilkov, G.. “Asymmetric Volatility Risk: Evidence from Option Markets.” Working Paper, University of Konstanz 2013.Google Scholar
Jouini, E., and Napp, C.. “Consensus Consumer and Intertemporal Asset Pricing with Heterogeneous Beliefs.” Review of Economic Studies, 74 (2007), 1149–1174.Google Scholar
Karatzas, I., and Shreve, S.. Brownian Motion and Stochastic Calculus. New York, NY: Springer-Verlag 1991.Google Scholar
Kogan, L.; Ross, S.; Wang, J.; and Westerfield, M.. “The Price Impact and Survival of Irrational Traders.” Journal of Finance, 61 (2006), 195–229.Google Scholar
Leland, H. “Who Should Buy Portfolio Insurance?” Journal of Finance, 35 (1980), 581–594.Google Scholar
Lin, Y.-N. “VIX Option Valuation.” Working Paper, National Chung Hsing University 2009.Google Scholar
Neftci, S. An Introduction to the Mathematics of Financial Derivatives. New York, NY: Academic Press 2007.Google Scholar
Patton, A., and Timmermann, A.. “Monotonicity in Asset Returns: New Tests with Applications to the Term Structure, the CAPM and Portfolio Sorts.” Journal of Financial Economics, 98 (2010), 605–625.Google Scholar
Rubinstein, M. “The Valuation of Uncertain Income Streams and the Pricing of Options.” Bell Journal of Economics, 7 (1976), 407–425.Google Scholar
Rubinstein, M. “Implied Binomial Trees.” Journal of Finance, 49 (1994), 771–818.Google Scholar
Sepp, A. “VIX Option Pricing in a Jump-Diffusion Model.” Risk, April (2008), 84–89.Google Scholar
Song, Z., and Xiu, D.. “A Tail of Two Option Markets: State-Price Densities and Volatility Risk.” Working Paper, Federal Reserve Board and University of Chicago (2013).Google Scholar
Todorov, V. “Variance Risk Premium Dynamics: The Role of Jumps.” Review of Financial Studies, 23 (2010), 345–383.Google Scholar
Xiong, W. “Bubbles, Crises, and Heterogeneous Beliefs.” Working Paper, Princeton University (2013).Google Scholar
Xiong, W., and Yan, H.. “Heterogeneous Expectations and Bond Markets.” Review of Financial Studies, 23 (2010), 1433–1466.CrossRefGoogle Scholar
Zhu, Y., and Zhang, J.. “Variance Term Structure and VIX Futures Pricing.” International Journal of Theoretical and Applied Finance, 10 (2007), 111–127.Google Scholar