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Parametric Inference and Dynamic State Recovery from Option Panels

  • Torben G. Andersen

    ()

    (Northwestern University, NBER, and CREATES)

  • Nicola Fusari

    ()

    (Northwestern University)

  • Viktor Todorov

    ()

    (Northwestern University)

We develop a new parametric estimation procedure for option panels observed with error which relies on asymptotic approximations assuming an ever increasing set of observed option prices in the moneyness-maturity (cross-sectional) dimension, but with a fixed time span. We develop consistent estimators of the parameter vector and the dynamic realization of the state vector that governs the option price dynamics. The estimators converge stably to a mixed-Gaussian law and we develop feasible estimators for the limiting variance. We provide semiparametric tests for the option price dynamics based on the distance between the spot volatility extracted from the options and the one obtained nonparametrically from high-frequency data on the underlying asset. We further construct new formal tests of the model t for specific regions of the volatility surface and for the stability of the risk-neutral dynamics over a given period of time. A large-scale Monte Carlo study indicates that the inference procedures work well for empirically realistic model specifications and sample sizes. In an empirical application to S&P 500 index options we extend the popular double-jump stochastic volatility model to allow for time-varying risk premia of extreme events, i.e., jumps, as well as a more exible relation between the risk premia and the level of risk. We show that both extensions provide a significantly improved characterization, both statistically and economically, of observed option prices.

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Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2012-11.

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Length: 49
Date of creation: 29 May 2011
Date of revision:
Handle: RePEc:aah:create:2012-11
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work so Well," CREATES Research Papers 2009-34, School of Economics and Management, University of Aarhus.
  2. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  3. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  4. Dean P. Foster & Daniel B. Nelson, 1994. "Continuous Record Asymptotics for Rolling Sample Variance Estimators," NBER Technical Working Papers 0163, National Bureau of Economic Research, Inc.
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  7. Neil Shephard & Ole Barndorff-Nielsen, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Series Working Papers 2004-FE-01, University of Oxford, Department of Economics.
  8. Donald W.K. Andrews, 2004. "Cross-section Regression with Common Shocks," Yale School of Management Working Papers ysm401, Yale School of Management.
  9. Viktor Todorov & George Tauchen, 2010. "Volatility Jumps," Working Papers 10-09, Duke University, Department of Economics.
  10. Tim Bollerslev & Viktor Todorov, 2010. "Tails, Fears and Risk Premia," Working Papers 10-33, Duke University, Department of Economics.
  11. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-70, September.
  12. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
  13. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  14. Pastorello, Sergio & Patilea, Valentin & Renault, Eric, 2003. "Iterative and Recursive Estimation in Structural Nonadaptive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 449-82, October.
  15. Patrick GAGLIARDINI & Christian GOURIEROUX & Eric RENAULT, 2004. "Efficient Derivative Pricing By The Extended Method of Moments," Swiss Finance Institute Research Paper Series 10-07, Swiss Finance Institute, revised Oct 2009.
  16. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
  17. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  18. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, 06.
  19. Peter Christoffersen & Kris Jacobs, 2003. "The Importance of the Loss Function in Option Valuation," CIRANO Working Papers 2003s-52, CIRANO.
  20. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  21. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
  22. Jean Jacod & Viktor Todorov, 2010. "Do price and volatility jump together?," Papers 1010.4990, arXiv.org.
  23. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  24. Pastorello, Sergio & Patilea, Valentin & Renault, Eric, 2003. "Iterative and Recursive Estimation in Structural Nonadaptive Models: Rejoinder," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 503-09, October.
  25. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-91, July.
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