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