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SPATIAL DEPENDENCE IN OPTION OBSERVATION ERRORS

Published online by Cambridge University Press:  13 April 2020

Torben G. Andersen ,
Nicola Fusari ,
Viktor Todorov  and
Rasmus T. Varneskov
Torben G. Andersen*
Affiliation:
Northwestern University, NBER, CREATES
Nicola Fusari
Affiliation:
The Johns Hopkins University Carey Business School
Viktor Todorov
Affiliation:
Northwestern University
Rasmus T. Varneskov
Affiliation:
Copenhagen Business School, CREATES, Multi Assets at Nordea Asset Management
*
Address correspondence to Torben G. Andersen, Department of Finance, Kellogg School of Management, Northwestern University, Evanston, IL60208, USA; e-mail: t-andersen@northwestern.edu.
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Abstract

In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau test for the null hypothesis of no spatial autocorrelation in the observation error. The test makes use of the smoothness of the true (unobserved) option price as a function of its strike and is robust to the presence of heteroskedasticity of unknown form in the observation error. A Monte Carlo study shows good finite-sample properties of the developed testing procedure and an empirical application to S&P 500 index option data reveals mild spatial dependence in the observation error, which has been declining in recent years.

Type
ET LECTURE
Information
Econometric Theory , Volume 37 , Issue 2 , April 2021 , pp. 205 - 247
Copyright
© Cambridge University Press 2020

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Footnotes

T.G.A. and R.T.V. gratefully acknowledge support from CREATES, Center for Research in Econometric Analysis of Time Series (DNRF78), funded by the Danish National Research Foundation. The work is partially supported by NSF Grant SES-1530748. We would like to thank the Editor (Peter C.B. Phillips) and two anonymous referees as well as participants at the 2019 SETA conference in Osaka, Japan for useful comments and suggestions.

References

REFERENCES

Andersen, T.G., Bondarenko, O. & Gonzalez-Perez, M.T. 2015a Exploring return dynamics via corridor implied volatility. The Review of Financial Studies 28(10), 2902–2945.CrossRefGoogle Scholar
Andersen, T.G., Fusari, N. & Todorov, V. 2015b Parametric inference and dynamic state recovery from option panels. Econometrica 83, 1081–1145.CrossRefGoogle Scholar
Andersen, T.G., Fusari, N. & Todorov, V. 2017 Short-term market risks implied by weekly options. The Journal of Finance 72(3), 1335–1386.CrossRefGoogle Scholar
Andersen, T.G., Fusari, N., Todorov, V. & Varneskov, R.T. 2019a Inference for option panels in pure-jump settings. Econometric Theory 35(5), 901–942.CrossRefGoogle Scholar
Andersen, T.G., Fusari, N., Todorov, V. & Varneskov, R.T. 2019b Unified inference for nonlinear factor models from panels with fixed and large time span. Journal of Econometrics 212(1), 4–25.CrossRefGoogle Scholar
Babaoglu, K., Christoffersen, P., Heston, S. & Jacobs, K. 2017 Option valuation with volatility components, fat tails, and nonmonotonic pricing kernels. The Review of Asset Pricing Studies 8(2), 183–231.CrossRefGoogle Scholar
Bakshi, G., Carr, P. & Wu, L. 2008 Stochastic risk premiums, stochastic skewness in currency options, and stochastic discount factors in international economies. Journal of Financial Economics 87(1), 132–156.CrossRefGoogle Scholar
Bakshi, G., Kapadia, N. & Madan, D. 2003 Stock return characteristics, skew laws, and the differential pricing of individual equity options. Review of Financial Studies 16, 101–143.CrossRefGoogle Scholar
Bakshi, G. & Madan, D. 2000 Spanning and derivative security valuation. Journal of Financial Economics 55, 205–238.Google Scholar
Bates, D.S. 1996 Jumps and stochastic volatility: Exchange rate processes implicit in deutsche mark options. Review of Financial Studies 9, 69–107.CrossRefGoogle Scholar
Bates, D.S. 2000 Post-’87 crash fears in S&P 500 future options. Journal of Econometrics 94, 181–238.CrossRefGoogle Scholar
Bates, D.S. 2003 Empirical option pricing: A retrospection. Journal of Econometrics 116, 387–404.Google Scholar
Berk, K.N. 1973 A central limit theorem for m-dependent random variables with unbounded m. The Annals of Probability 1(2), 352–354.CrossRefGoogle Scholar
Black, F. & Scholes, M. 1973 The pricing of options and corporate liabilities. Journal of Political Economy 81(3), 637–654.Google Scholar
Bollerslev, T. & Todorov, V. 2011 Tails, fears and risk premia. Journal of Finance 66, 2165–2211.Google Scholar
Bollerslev, T., Todorov, V. & Xu, L. 2015 Tail risk premia and return predictability. Journal of Financial Economics 118(1), 113–134.CrossRefGoogle Scholar
Box, G.E.P. & Pierce, D.A. 1970 Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association 65(332), 1509–1526.CrossRefGoogle Scholar
Britten-Jones, M. & Neuberger, A. 2000 Option prices, implied price processes, and stochastic volatility. Journal of Finance 55, 839–866.Google Scholar
Broadie, M., Chernov, M. & Johannes, M. 2007 Specification and risk premiums: The information in S&P 500 futures options. Journal of Finance 62, 1453–1490.CrossRefGoogle Scholar
Brockwell, P.J. & Davis, R.A. 1991 Time Series: Theory and Methods, 2nd ed. Springer Verlag.CrossRefGoogle Scholar
Carr, P. & Madan, D. 2001 Optimal positioning in derivative securities. Quantitative Finance 1, 19–37.CrossRefGoogle Scholar
Carr, P. & Wu, L. 2007 Stochastic skew in currency options. Journal of Financial Economics 86(1), 213–247.Google Scholar
Carr, P. & Wu, L. 2009 Variance risk premia. Review of Financial Studies 22, 1311–1341.CrossRefGoogle Scholar
Christoffersen, P., Jacobs, K. & Ornthanalai, C. 2012 Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options. Journal of Financial Economics 106(3), 447–472.CrossRefGoogle Scholar
Conley, T. 1999 GMM estimation with cross sectional dependence. Journal of Econometrics 92, 1–45.CrossRefGoogle Scholar
Dalla, V., Giraitis, L. & Phillips, P.C.B. 2019 Robust Tests for White Noise and Cross-Correlation. Cowles Foundation Discussion Paper.Google Scholar
Delgado, M.A. & Robinson, P.M. 2015 Non-nested testing of spatial correlation. Journal of Econometrics 187(1), 385–401.CrossRefGoogle Scholar
Duffie, D., Pan, J. & Singleton, K. 2000 Transform analysis and asset pricing for affine jump-diffusions. Econometrica 68, 1343–1376.CrossRefGoogle Scholar
Eraker, B. 2004 Do stock prices and volatility jump? Reconciling evidence from spot and option prices. Journal of Finance 59, 1367–1403.CrossRefGoogle Scholar
Gagliardini, P., Gourieroux, C. & Renault, E. 2011 Efficient derivative pricing by the extended method of moments. Econometrica 79, 1181–1232.Google Scholar
Gupta, A. & Robinson, P.M. 2015 Inference on higher-order spatial autoregressive models with increasingly many parameters. Journal of Econometrics 186(1), 19–31.CrossRefGoogle Scholar
Gupta, A. & Robinson, P.M. 2018 Pseudo maximum likelihood estimation of spatial autoregressive models with increasing dimension. Journal of Econometrics 202(1), 92–107.CrossRefGoogle Scholar
Heston, S.L. 1993 A closed-form solution for options with stochastic volatility with applications to bond and currency options. The Review of Financial Studies 6(2), 327–343.CrossRefGoogle Scholar
Jacod, J., Li, Y. & Zheng, X. 2017 Statistical properties of microstructure noise. Econometrica 85(4), 1133–1174.CrossRefGoogle Scholar
Jenish, N. & Prucha, I.R. 2012 On spatial processes and asymptotic inference under near-epoch dependence. Journal of Econometrics 170(1), 178–190.Google ScholarPubMed
Kelejian, H.H. & Prucha, I.R. 1999 A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40(2), 509–533.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. 2007 HAC estimation in a spatial framework. Journal of Econometrics 140(1), 131–154.CrossRefGoogle Scholar
Kelejian, H.H. & Prucha, I.R. 2010 Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances. Journal of Econometrics 157(1), 53–67.CrossRefGoogle ScholarPubMed
Kuersteiner, G.M. & Prucha, I.R. 2013 Limit theory for panel data models with cross sectional dependence and sequential exogeneity. Journal of Econometrics 174(2), 107–126.CrossRefGoogle ScholarPubMed
Lee, L.-F. 2002 Consistency and efficiency of least squares estimation for mixed regressive, spatial autoregressive models. Econometric Theory 18(2), 252–277.CrossRefGoogle Scholar
Lee, L.-F. 2003 Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances. Econometric Reviews 22(4), 307–335.Google Scholar
Lee, L.-F. 2004 Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models. Econometrica 72(6), 1899–1925.CrossRefGoogle Scholar
Lee, L.-F. & Liu, X. 2010 Efficient GMM estimation of high order spatial autoregressive models with autoregressive disturbances. Econometric Theory 26(1), 187–230.CrossRefGoogle Scholar
Ljung, G.M. & Box, G.E.P. 1978 On a measure of lack of fit in time series models. Biometrika 65(2), 297–303.CrossRefGoogle Scholar
Pan, J. 2002 The jump-risk premia implicit in options: Evidence from an integrated time-series study. Journal of Financial Economics 63, 3–50.CrossRefGoogle Scholar
Pastorello, S., Patilea, V. & Renault, E. 2003 Iterative and recursive estimation in structural nonadaptive models. Journal of Business and Economic Statistics 21, 449–482.CrossRefGoogle Scholar
Qin, L. & Todorov, V. 2019 Nonparametric implied Lévy densities. The Annals of Statistics 47(2), 1025–1060.CrossRefGoogle Scholar
Renault, E. 1997 Econometric models of option pricing. In Kreps, D. & Wallis, K. (eds.), Advances in Economics and Econometrics, Seventh World Congress, pp. 223–278. Cambridge University Press.Google Scholar
Robinson, P.M. 2008 Correlation testing in time series, spatial and cross-sectional data. Journal of Econometrics 147(1), 5–16.CrossRefGoogle Scholar
Robinson, P.M. 2010 Efficient estimation of the semiparametric spatial autoregressive model. Journal of Econometrics 157(1), 6–17.Google Scholar
Robinson, P.M. 2011 Asymptotic theory for nonparametric regression with spatial data. Journal of Econometrics 165(1), 5–19.Google Scholar
Robinson, P.M. & Thawornkaiwong, S. 2012 Statistical inference on regression with spatial dependence. Journal of Econometrics 167(2), 521–542.Google Scholar
Schneider, P. & Trojani, F. 2019 Divergence and the price of uncertainty. Journal of Financial Econometrics 17, 341–396.CrossRefGoogle Scholar
Su, L. & Jin, S. 2010 Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models. Journal of Econometrics 157(1), 18–33.CrossRefGoogle Scholar
Todorov, V. 2019 Nonparametric option-implied volatility. The Annals of Applied Probability. 29(6), 3590–3636.CrossRefGoogle Scholar
Varneskov, R.T. 2017 Estimating the quadratic variation spectrum of noisy asset prices using generalized flat-top realized kernels. Econometric Theory 33(6), 1457–1501.Google Scholar
Xu, X. & Lee, L.-F. 2015 A spatial autoregressive model with a nonlinear transformation of the dependent variable. Journal of Econometrics 186(1), 1–18.CrossRefGoogle Scholar