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Statistical Inference for Random Variance Option Pricing

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  • S, Pastorello

    (Crest)

  • E, Renault

    (Crest)

  • N, Touzi

    (Crest)

Abstract

This article deals with the estimation of continuous-time stochastic volatility models of option pricing. We argue that option prices are much more informative about the parameters than are asset prices. This is confirmed in a Monte Carlo experiment that compares two very simple strategies based on the different information sets. Both approaches are based on indirect inference and avoid any discretization bias by simulating the continuous-time model. We assume an Ornstein-Uhlenbeck process for the log of the volatility, a zero-volatility risk premium, and no leverage effect. We do not pursue asymptotic efficiency or specification issues; rather, we stick to a framework with no overidentifying restrictions and show that, given our option-pricing model, estimation based on option prices is much more precise in samples of typical size, without increasing the computational burden.

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Bibliographic Info

Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 97-60.

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Date of creation: 1997
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Handle: RePEc:crs:wpaper:97-60

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Cited by:
  1. Antonio Mele & Filippo Altissimo, 2004. "Simulated Nonparametric Estimation of Continuous Time Models of Asset Prices and Returns," FMG Discussion Papers dp476, Financial Markets Group.
  2. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
  3. Jeremy Graveline & Irina Zviadadze & Mikhail Chernov, 2012. "Crash Risk in Currency Returns," 2012 Meeting Papers 753, Society for Economic Dynamics.
  4. F. Comte & L. Coutin & E. Renault, 2012. "Affine fractional stochastic volatility models," Annals of Finance, Springer, vol. 8(2), pages 337-378, May.
  5. Sergio Pastorello & Valentin Patilea & Éric Renault, 2003. "Iterative and Recursive Estimation in Structural Non-Adaptive Models," CIRANO Working Papers 2003s-08, CIRANO.
  6. Cheng, Ai-ru (Meg) & Gallant, A. Ronald & Ji, Chuanshu & Lee, Beom S., 2008. "A Gaussian approximation scheme for computation of option prices in stochastic volatility models," Journal of Econometrics, Elsevier, vol. 146(1), pages 44-58, September.
  7. Garcia, René & Lewis, Marc-André & Pastorello, Sergio & Renault, Éric, 2011. "Estimation of objective and risk-neutral distributions based on moments of integrated volatility," Journal of Econometrics, Elsevier, vol. 160(1), pages 22-32, January.
  8. F. Fornari & A. Mele, 1998. "ARCH Models and Option Pricing : The Continuous Time Connection," THEMA Working Papers 98-30, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  9. Max O. Souza & Jorge P. Zubelli, 2007. "On The Asymptotics Of Fast Mean-Reversion Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(05), pages 817-835.
  10. Li, Tong, 2010. "Indirect inference in structural econometric models," Journal of Econometrics, Elsevier, vol. 157(1), pages 120-128, July.
  11. A. S. Hurn & K. A. Lindsay & V. L. Martin, 2003. "On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 45-63, 01.
  12. Raknerud, Arvid & Skare, Øivind, 2012. "Indirect inference methods for stochastic volatility models based on non-Gaussian Ornstein–Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3260-3275.
  13. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, 06.
  14. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.

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