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What Data Should Be Used to Price Options?

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  • Mikhail Chernov
  • Eric Ghysels

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Abstract

In this paper we propose a generic procedure for estimating and pricing options in the context of stochastic volatility models using simultaneously the fundamental price and a set of option contracts. We appraise univariate and multivariate estimation of the model in terms of pricing and hedging performance. Our results, based on the S&P 500 index contract, show that the univariate approach only involving options by and large dominates. A by-product of this finding is that we uncover a remarkably simple volatility extraction filter based on a polynomial lag structure of implied volatilities. The bivariate approach involving both the fundamental and an option appears useful when the information from the cash market provides support via the conditional kurtosis to price options. This is the case for some long-term options. Moreover, having estimated separately the risk-neutral and objective measures allows us to appraise the typical risk-neutral representations used in the literature. Using Heston's (1993) model as example we show that the usual transformation from objective to risk neutral density is not supported by the data. Nous présentons une procédure générique pour l'estimation et l'évaluation de modèles d'options avec volatilité stochastique où le sousjacent et un ensemble de contrats d'options sont utilisés simultanément. Nos résultats démontrent qu'un modèle univarié avec seulement des données d'options domine en terme d'erreurs de prix hors-échantillon et en terme de couverture. Nous trouvons également un filtre d'extraction pour la volatilité latente qui est basé sur un polynome de retards de volatilités implicites. Ayant simultanément la probabilité de risque neutre et la probabilité objective, nous pouvons vérifier, dans le contexte du modèle de Heston, si la transformation usuelle est empiriquement plausible. Nous rejetons le changement de mesure supposé dans ce modèle.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 98s-22.

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Date of creation: 01 Jun 1998
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Handle: RePEc:cir:cirwor:98s-22

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Keywords: Derivative securities; efficient method of moments; state price densities; stochastic volatility models; filtering; Titres dérivés; méthode de moments efficaces; prix d'états; filtrage; volatilité stochastique;

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References

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  1. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  2. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc.
  3. Victor Fenton & Gallant, A. Ronald, 1996. "Qualitative and Asymptotic Performance of SNP Density Estimators," Working Papers 96-17, Duke University, Department of Economics.
  4. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
  5. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1997. "Estimation of stochastic volatility models with diagnostics," Journal of Econometrics, Elsevier, vol. 81(1), pages 159-192, November.
  6. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
  7. Hansen, Lars Peter & Jagannathan, Ravi, 1991. "Implications of Security Market Data for Models of Dynamic Economies," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 225-62, April.
  8. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  9. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
  10. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  11. Eric Jacquier & Robert Jarrow, . "Model Error in Contingent Claim Models (Dynamic Evaluation)," Rodney L. White Center for Financial Research Working Papers 07-96, Wharton School Rodney L. White Center for Financial Research.
  12. Nelson, Daniel B., 1996. "Asymptotic filtering theory for multivariate ARCH models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 1-47.
  13. Eric Jacquier & Nicholas G. Polson & Peter Rossi, . "Stochastic Volatility: Univariate and Multivariate Extensions," Rodney L. White Center for Financial Research Working Papers 19-95, Wharton School Rodney L. White Center for Financial Research.
  14. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
  15. Nelson, Daniel B & Foster, Dean P, 1994. "Asymptotic Filtering Theory for Univariate ARCH Models," Econometrica, Econometric Society, vol. 62(1), pages 1-41, January.
  16. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  17. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  18. repec:fth:inseep:9338 is not listed on IDEAS
  19. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  20. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(04), pages 657-681, October.
  21. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
  22. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
  23. Ait-Sahalia, Yacine & Wang, Yubo & Yared, Francis, 2001. "Do option markets correctly price the probabilities of movement of the underlying asset?," Journal of Econometrics, Elsevier, vol. 102(1), pages 67-110, May.
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Citations

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Cited by:
  1. Broadie, Mark & Detemple, Jerome & Ghysels, Eric & Torres, Olivier, 2000. "Nonparametric estimation of American options' exercise boundaries and call prices," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1829-1857, October.
  2. Gabriele Fiorentini & Angel León & Gonzalo Rubio, . "Short-term options with stochastic volatility: Estimation and empirical performance," Studies on the Spanish Economy 02, FEDEA.
  3. Torben Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," NBER Working Papers 6961, National Bureau of Economic Research, Inc.
  4. Darrell Duffie & Jun Pan & Kenneth Singleton, 1999. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," NBER Working Papers 7105, National Bureau of Economic Research, Inc.

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