×

Skewness term-structure tests. (English) Zbl 1396.91746

Summary: In this paper, we conduct skewness term-structure tests to check whether the temporal structure of risk-neutral skewness is consistent with rational expectations. Because risk-neutral skewness is substantially mean reverting, skewness shocks should decay quickly and risk-neutral skewness of more distant option should display the rationally expected smoothing behaviour. Using an equilibrium asset and option-pricing model in a production economy under jump diffusion with stochastic jump intensity, we derive this elasticity analytically. In an empirical application of the model using more than 20 years of data on S&P500 index options, we find that this elasticity turns out to be different than suggested under rational expectations – smaller on the short end (underreaction) and larger on the long end (overreaction) of the ’skewness curve’.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60J75 Jump processes (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ahn, D.-H., R. F. Dittmar, and A. R. Gallant. 2002. “Quadratic Term Structure Models: Theory and Evidence.” Review of Finanical Studies 15: 243-288. doi:10.1093/rfs/15.1.243.
[2] Bakshi, G., N. Kapadia, and D. Madan. 2003. “Stock Return Characteristics, Skew Laws, and Differential Pricing of Individual Equity Options.” Review of Financial Studies 16: 101-143. doi:10.1093/rfs/16.1.0101.
[3] Chang, B. Y., P. Christoffersen, and K. Jacobs. 2013. “Market Skewness Risk and the Cross Section of Stock Returns.” Journal of Financial Economics 107 (1): 46-68. doi:10.1016/j.jfineco.2012.07.002.
[4] Christoffersen, P., K. Jacobs, and C. Ornthanalai. 2012. “Dynamics Jump Intensities and Risk Premiums: Evidence from S&P 500 Returns and Options.” Journal of Financial Economics 106 (3): 447-472. doi:10.1016/j.jfineco.2012.05.017.
[5] Christoffersen, P., S. Heston, and K. Jacobs. 2013. “Capturing Option Anomalies with a Variance-Dependent Pricing Kernel.” The Review of Financial Studies 26 (8): 1963-2006. doi:10.1093/rfs/hht033.
[6] Conrad, J., R. F. Dittmar, and E. Ghysels. 2013. “Ex Ante Skewness and Expected Stock Returns.” The Journal of Finance 68 (1): 85-124. doi:10.1111/j.1540-6261.2012.01795.x.
[7] Duffie, D., J. Pan, and K. Singleton. 2000. “Transform Analysis and Asset Pricing for Affine Jump-Diffusion.” Econometrica 68: 1343-1376. doi:10.1111/ecta.2000.68.issue-6. · Zbl 1055.91524
[8] Harvey, C. R., and A. Siddique. 1999. “Autogressive Conditional Skewness.” Journal of Financial and Quantitative Analysis 34: 465-487. doi:10.2307/2676230.
[9] Harvey, C. R., and A. Siddique. 2000a. “Time-Varying Conditional Skewness and the Market Risk Premium.” Research in Banking and Finance 1: 27-60.
[10] Harvey, C. R., and A. Siddique. 2000b. “Conditional Skewness in Asset Pricing Tests.” The Journal of Finance 55: 1263-1295. doi:10.1111/0022-1082.00247.
[11] Kraus, A., and R. H. Litzenberger. 1976. “Skewness Preference and the Valuation of Risk Assets.” Journal of Finance 4: 1085-1100.
[12] Lehnert, T., Y. Lin, and C. Wolff (2013). Skewness Risk Premium: Theory and Empirical Evidence. Working paper. Centre for Economic Policy Research (CEPR).
[13] Merton, R. C.1973. “An Intertemporal Capital Asset Pricing Model.” Econometrica 41 (5): 867-887. doi:10.2307/1913811. · Zbl 0283.90003
[14] Poterba, J. M., and L. H. Summers. 1986. “The Persistence of Volatility and Stock Market Fluctuations.” American Economic Review 76: 1142-1151.
[15] Poteshman, A. M.2001. “Underreaction, Overreaction, and Increasing Misreaction to Information in the Options Market.” The Journal of Finance 56: 851-876. doi:10.1111/0022-1082.00348.
[16] Santa-Clara, P., and S. Yan. 2010. “Crashes, Volatility, and the Equity Premium: Lessons from S&P 500 Options.” The Review of Economics and Statistics 92 (2): 435-451. doi:10.1162/rest.2010.11549.
[17] Symmonds, M., N. D. Wright, D. R. Bach, and R. J. Dolan. 2011. “Deconstructing Risk: Separable Encoding of Variance and Skewness in the Brain.” NeuroImage 58: 1139-1149. doi:10.1016/j.neuroimage.2011.06.087.
[18] Stein, J.1989. “Overreactions in the Options Market.” The Journal of Finance 44 (4): 1011-1023. doi:10.1111/j.1540-6261.1989.tb02635.x.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.