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Assessing the quality of volatility estimators via option pricing

Author

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  • Sanfelici Simona

    () (University of Parma, Department of Economics, Via J.F. Kennedy 6, 43125 Parma, Italy)

  • Uboldi Adamo

    (European Commission, DG AGRI, Unit L2 Economic Analysis, Brussels, Belgium)

Abstract

The aim of this paper is to measure and assess the accuracy of different volatility estimators based on high frequency data in an option pricing context. For this, we use a discrete-time stochastic volatility model based on Auto-Regressive-Gamma (ARG) dynamics for the volatility. First, ARG processes are presented both under historical and risk-neutral measure, in an affine stochastic discount factor framework. The model parameters are estimated exploiting the informative content of historical high frequency data. Secondly, option pricing is performed via Monte Carlo techniques. This framework allows us to measure the quality of different volatility estimators in terms of mispricing with respect to real option data, leaving to the ARG volatility model the role of a tool. Our analysis points out that using high frequency intra-day returns allows to obtain more accurate ex post estimation of the true (unobservable) return variation than do the more traditional sample variances based on daily returns, and this is reflected in the quality of pricing. Moreover, estimators robust to microstructure effects show an improvement over the realized volatility estimator. The empirical analysis is conducted on European options written on S&P500 index.

Suggested Citation

  • Sanfelici Simona & Uboldi Adamo, 2014. "Assessing the quality of volatility estimators via option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(2), pages 1-22, April.
  • Handle: RePEc:bpj:sndecm:v:18:y:2014:i:2:p:22:n:3
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    References listed on IDEAS

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    1. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    2. Christoffersen, Peter & Feunou, Bruno & Jacobs, Kris & Meddahi, Nour, 2014. "The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(03), pages 663-697, June.
    3. Mancino Maria Elvira & Simona Sanfelici, 2009. "Covariance estimation and dynamic asset allocation under microstructure effects via Fourier methodology," Working Papers - Mathematical Economics 2009-09, Universita' degli Studi di Firenze, Dipartimento di Scienze per l'Economia e l'Impresa.
    4. Joann Jasiak & Christian Gourieroux, 2006. "Autoregressive gamma processes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 129-152.
    5. 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 327-343.
    6. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, February.
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