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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. Nelson, Daniel B., 1996. "Asymptotic filtering theory for multivariate ARCH models," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 1-47.
  2. Lars Peter Hansen & Ravi Jagannathan, 1990. "Implications of Security Market Data for Models of Dynamic Economies," NBER Technical Working Papers 0089, National Bureau of Economic Research, Inc.
  3. Eric Jacquier & Nicholas G. Polson & Peter Rossi, 1999. "Stochastic Volatility: Univariate and Multivariate Extensions," Computing in Economics and Finance 1999 112, Society for Computational Economics.
  4. Gallant, A.R. & Tauchen, G., 1988. "Seminonparametric Estimation Of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Papers 88-59, Chicago - Graduate School of Business.
  5. Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
  6. Fenton, Victor M. & Gallant, A. Ronald, 1996. "Qualitative and asymptotic performance of SNP density estimators," Journal of Econometrics, Elsevier, vol. 74(1), pages 77-118, September.
  7. 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.
  8. repec:fth:inseep:9338 is not listed on IDEAS
  9. Daniel B. Nelson & Dean P. Foster, 1994. "Asypmtotic Filtering Theory for Univariate Arch Models," NBER Technical Working Papers 0129, National Bureau of Economic Research, Inc.
  10. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
  11. 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.
  12. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  13. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  14. 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.
  15. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  16. 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.
  17. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  18. 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.
  19. Eric Jacquier & Robert Jarrow, . "Model Error in Contingent Claim Models (Dynamic Evaluation)," Rodney L. White Center for Financial Research Working Papers 7-96, Wharton School Rodney L. White Center for Financial Research.
  20. 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.
  21. 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.
  22. Gallant, A. Ronald & Hsieh, David & Tauchen, George, 1995. "Estimation of Stochastic Volatility Models with Diagnostics," Working Papers 95-36, Duke University, Department of Economics.
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Cited by:
  1. Ángel León & Gabriele Fiorentini & Gonzalo Rubio, 2000. "Short-Term Options With Stochastic Volatility: Estimation And Empirical Performance," Working Papers. Serie AD 2000-25, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  2. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 1999. "The Distribution of Exchange Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-059, New York University, Leonard N. Stern School of Business-.
  3. 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.
  4. Mark Broadie & Jérôme B. Detemple & Eric Ghysels & Olivier Torrès, 1996. "Nonparametric Estimation of American Options Exercise Boundaries and Call Prices," CIRANO Working Papers 96s-24, CIRANO.

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