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TESTING FOR ANTICIPATED CHANGES IN SPOT VOLATILITY AT EVENT TIMES

Published online by Cambridge University Press:  19 May 2023

Viktor Todorov  and
Yang Zhang
Viktor Todorov*
Affiliation:
Northwestern University
Yang Zhang
Affiliation:
Financial Market Infrastructure Firm
*
Address correspondence to Viktor Todorov, Department of Finance, Kellogg School of Management, Northwestern University, Evanston, IL, USA; e-mail: v-todorov@kellogg.northwestern.edu.
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Abstract

We propose a test for anticipated changes in spot volatility, either due to continuous or discontinuous price moves, at the times of realization of event risk in the form of pre-scheduled releases of economic information such as earnings announcements by firms and macroeconomic news announcements. These events can generate nontrivial volatility in asset returns, which does not scale even locally in time. Our test is based on short-dated options written on an underlying asset subject to event risk, which takes place after the options’ observation time and prior to or after their expiration. We use options with different tenors to estimate the conditional (risk-neutral) characteristic functions of the underlying asset log-returns over the horizons of the options. Using these estimates and a relationship between the conditional characteristic functions with three different tenors, which holds true if and only if continuous and discontinuous spot volatility does not change at the event time, we design a test for this hypothesis. In an empirical application, we study anticipated individual stocks’ volatility changes following earnings announcements for a set of stocks with good option coverage.

Type
ET LECTURE
Information
Econometric Theory , First View , pp. 1 - 34
Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

We would like to thank the Editor (Peter C.B. Phillips), the Co-Editor (Eric Renault), and three anonymous referees, as well as participants at the 2022 SETA Virtual conference for many useful comments and suggestions. Yang Zhang completed the work in her personal time. The views expressed in this paper are strictly those of the authors and do not represent the opinion of Yang Zhang’s employer.

References

REFERENCES

Ai, H. & Bansal, R. (2018) Risk preferences and the macroeconomic announcement premium. Econometrica 86(4), 1383–1430.CrossRefGoogle Scholar
Aït-Sahalia, Y. & Jacod, J. (2014) High-frequency financial econometrics. In High-Frequency Financial Econometrics. Princeton University Press.Google Scholar
Andersen, T.G., Bollerslev, T., Diebold, F.X., & Labys, P. (2003) Modeling and forecasting realized volatility. Econometrica 71, 579–625.CrossRefGoogle Scholar
Andersen, T.G., Fusari, N., & Todorov, V. (2015) Parametric inference and dynamic state recovery from option panels. Econometrica 83, 1081–1145.CrossRefGoogle Scholar
Andersen, T.G., Fusari, N., Todorov, V., & Varneskov, R.T. (2021) Spatial dependence in option observation errors. Econometric Theory 37(2), 205–247.CrossRefGoogle Scholar
Bandi, F.M. & Phillips, P.C.B. (2003) Fully nonparametric estimation of scalar diffusion models. Econometrica 71(1), 241–283.CrossRefGoogle Scholar
Barndorff-Nielsen, O. & Shephard, N. (2002) Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 64(2), 253–280.CrossRefGoogle Scholar
Barndorff-Nielsen, O. & Shephard, N. (2004a) Econometric analysis of realized covariation: High frequency based covariance, regression, and correlation in financial economics. Econometrica 72(3), 885–925.CrossRefGoogle Scholar
Barndorff-Nielsen, O. & Shephard, N. (2004b) Power and Bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics 2, 1–37.CrossRefGoogle Scholar
Barndorff-Nielsen, O. & Shephard, N. (2006) Econometrics of testing for jumps in financial economics using Bipower variation. Journal of Financial Econometrics 4, 1–30.CrossRefGoogle Scholar
Bates, D.S. (2003) Empirical option pricing: A retrospection. Journal of Econometrics 116(1–2), 387–404.CrossRefGoogle Scholar
Bernanke, B.S. & Kuttner, K.N. (2005) What explains the stock market’s reaction to federal reserve policy? Journal of Finance 60(3), 1221–1257.CrossRefGoogle Scholar
Black, F. & Scholes, M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–654.CrossRefGoogle Scholar
Bollerslev, T. & Zhou, H. (2002) Estimating stochastic volatility diffusion using conditional moments of integrated volatility. Journal of Econometrics 109(1), 33–65.CrossRefGoogle Scholar
Breeden, D.T. & Litzenberger, R.H. (1978) Prices of state-contingent claims implicit in option prices. Journal of Business 51, 621–651.CrossRefGoogle Scholar
Carr, P. & Madan, D. (2001) Optimal positioning in derivative securities. Quantitiative Finance 1, 19–37.CrossRefGoogle Scholar
Cerovecki, C. & Hörmann, S. (2017) On the CLT for discrete Fourier transforms of functional time series. Journal of Multivariate Analysis 154, 282–295.CrossRefGoogle Scholar
Cochrane, J.H. & Piazzesi, M. (2002) The fed and interest rates—A high-frequency identification. American Economic Review 92(2), 90–95.CrossRefGoogle Scholar
Corradi, V. & Distaso, W. (2006) Semi-parametric comparison of stochastic volatility models using realized measures. Review of Economic Studies 73(3), 635–667.CrossRefGoogle Scholar
Da, Z. & Warachka, M.C. (2009) Cashflow risk, systematic earnings revisions, and the cross-section of stock returns. Journal of Financial Economics 94(3), 448–468.CrossRefGoogle Scholar
Dubinsky, A., Johannes, M., Kaeck, A., & Seeger, N.J. (2019) Option pricing of earnings announcement risks. Review of Financial Studies 32(2), 646–687.CrossRefGoogle Scholar
Duffie, D. (2001) Dynamic Asset Pricing Theory, 3rd Edition. Princeton University Press.Google Scholar
Durrleman, V. (2008) Convergence of at-the-money implied volatilities to the spot volatility. Journal of Applied Probability 45(2), 542–550.CrossRefGoogle Scholar
Eraker, B. (2004) Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance 59(3), 1367–1403.CrossRefGoogle Scholar
Jacod, J. & Shiryaev, A. (2003) Limit Theorems for Stochastic Processes, 2nd Edition. Springer.CrossRefGoogle Scholar
Jacod, J. & Todorov, V. (2010) Do price and volatility jump together? Annals of Applied Probability 20(4), 1425–1469.CrossRefGoogle Scholar
Jeon, Y., McCurdy, T.H., & Zhao, X. (2022) News as sources of jumps in stock returns: Evidence from 21 million news articles for 9000 companies. Journal of Financial Economics 145(2), 1–17.CrossRefGoogle Scholar
Lucca, D.O. & Moench, E. (2015) The pre-FOMC announcement drift. Journal of Finance 70(1), 329–371.CrossRefGoogle Scholar
Medvedev, A. & Scaillet, O. (2007) Approximation and calibration of short-term implied volatilities under jump-diffusion stochastic volatility. Review of Financial Studies 20(2), 427–459.CrossRefGoogle Scholar
Nakamura, E. & Steinsson, J. (2018) Identification in macroeconomics. Journal of Economic Perspectives 32(3), 59–86.CrossRefGoogle Scholar
Pan, J. (2002) The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics 63(1), 3–50.CrossRefGoogle Scholar
Rigobon, R. & Sack, B. (2004) The impact of monetary policy on asset prices. Journal of Monetary Economics 51(8), 1553–1575.CrossRefGoogle Scholar
Sato, K. (1999) Lévy Processes and Infinitely Divisible Distributions. Cambridge University Press.Google Scholar
Savor, P. & Wilson, M. (2014) Asset pricing: A tale of two days. Journal of Financial Economics 113, 171–201.CrossRefGoogle Scholar
Savor, P. & Wilson, M. (2016) Earnings announcements and systematic risk. Journal of Finance 71(1), 83–138.CrossRefGoogle Scholar
Todorov, V. (2009) Estimation of continuous-time stochastic volatility models with jumps using high-frequency data. Journal of Econometrics 148(2), 131–148.CrossRefGoogle Scholar
Todorov, V. (2019) Nonparametric spot volatility from options. Annals of Applied Probability 29(6), 3590–3636.CrossRefGoogle Scholar
Todorov, V. (2020) Testing and inference for fixed times of discontinuity in semimartingales. Bernoulli 26(4), 2907–2948.CrossRefGoogle Scholar
Todorov, V. & Zhang, Y. (2022) Information gains from using short-dated options for measuring and forecasting volatility. Journal of Applied Econometrics 37(2), 368–391.CrossRefGoogle Scholar
van der Vaart, A.W. & Wellner, J. (1996) Weak Convergence and Empirical Processes. Springer.CrossRefGoogle Scholar