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Studies in Nonlinear Dynamics & Econometrics

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Volume 18, Issue 2

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Assessing the quality of volatility estimators via option pricing

Simona Sanfelici / Adamo Uboldi
Published Online: 2013-07-16 | DOI: https://doi.org/10.1515/snde-2012-0075

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.

This article offers supplementary material which is provided at the end of the article.

Keywords: high-frequency data; volatility estimation; option pricing

References

  • Aït-Sahalia, Y., and A. W. Lo. 1998. “Nonparametric Estimation of State-price Densities Implicit in Financial Asset Prices.” The Journal of Finance 53 (2): 499–547.CrossrefGoogle Scholar

  • Aït-Sahalia, Y., P. Mykland, and L. Zhang. 2005. “How Often to Sample A Continuous-time Process in the Presence of Market Microstructure Noise.” Review of Financial Studies 18: 351–416.Google Scholar

  • Bakshi, G., C. Cao, and Z. Chen. 1997. “Empirical Performance of Alternative Option Pricing Models.” The Journal of Finance 52 (5): 2003–2049.CrossrefGoogle Scholar

  • Band, F., J. R. Russell, and C. Yang. 2008. “Realized Volatility Forecasting and Option Pricing.” Journal of Econometrics 147: 34–46.Web of ScienceGoogle Scholar

  • Bandi, F. M., and J. R. Russel. 2006a. “Separating Market Microstructure Noise from Volatility.” Journal of Financial Economics 79: 655–692.CrossrefGoogle Scholar

  • Bandi, F. M., and J. R. Russell. 2006b. “Market Microstructure Noise, Integrated Variance Estimators, and the Accuracy of Asymptotic Approximations.” Working Paper, University of Chicago.http://faculty.chicagogsb.edu/federicobandi.Web of Science

  • Bandi, F. M., J. R. Russel, and Y. Zhu. 2008. “Using High-Frequency Data in Dynamic Portfolio Choice.” Econometric Reviews 27 (1–3): 163–198.CrossrefWeb of ScienceGoogle Scholar

  • Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard. 2008a. “Designing Realised Kernels to Measure the Ex-post Variation of Equity Prices in the Presence of Noise.” Econometrica 76/6: 1481–1536.Web of ScienceGoogle Scholar

  • Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard. 2008b. “Multivariate Realised Kernels: Consistent Positive Semi-definite Estimators of the Covariation of Equity Prices with Noise and Non-Synchronous Trading. Working paper.Web of ScienceGoogle Scholar

  • Barndorff-Nielsen, O. E., P. R. Hansen, A. Lunde, and N. Shephard. 2011. “Subsampling Realised Kernels.” Journal of Econometrics 160 (1): 204–219.CrossrefWeb of ScienceGoogle Scholar

  • Bates, D. 2000. “Post-87 Crash Fears in S&P 500 Futures Option Market.” Journal of Econometrics 94 (1/2): 181–238.CrossrefGoogle Scholar

  • Black, F., and M. Scholes. 1973. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy 81: 659–683.Google Scholar

  • Brent, R. P. 1973. Algorithms for Minimization without Derivatives. Englewood Cliffs, New Jersey: Prentice-Hall.Google Scholar

  • Carr, P., and B. Madan. 1999. “Option Valuation using the Fast Fourier Transform. Journal of Computational Finance 2/4: 61–73.Google Scholar

  • Christoffersen, P., B. Feunou, K. Jacobs, and N. Meddahi. 2011. “The Economic Value of Realized Volatility: Using High-Frequency Returns for Option Valuation.” Working Paper.Google Scholar

  • Corsi, F., D. Pirino, and R. Renó. 2009. “Threshold Bipower Variation and the Impact of Jumps on Volatility Forcasting.” Working Paper, 1–31.Google Scholar

  • Corsi, F., N. Fusari, and D. La Vecchia. 2012. “Realizing Smiles: Options Pricing with Realized Volatility.” Journal of Financial Economics. 107 (2): 284–304.Web of ScienceGoogle Scholar

  • De Pooter, M., M. Martens, and Dick van Dijk. 2008. “Predicting the Daily Covariance Matrix for S&P100 Stocks Using Intra-day Data: But Which Frequency to Use?” Econometric Reviews 27: 199–229.CrossrefWeb of ScienceGoogle Scholar

  • Dumas, B., J. Fleming, and R. E. Whaley. 1998. “Implied Volatility Functions: Empirical Tests.” The Journal of Finance 53 (6): 2059–2106.CrossrefGoogle Scholar

  • Fleming, J., C. Kirby, and B. Ostdiek. 2001a. “The Economic Value of Volatility Timing.” The Journal of Finance LVI (1): 329–352.Google Scholar

  • Fleming, J., C. Kirby, and B. Ostdiek. 2001b. “The Economic Value of Volatility Timing Using “Realized” Volatility.” The Journal of Financial Economics 67: 473–509.Google Scholar

  • Forsythe, G. E., M. A. Malcolm, and C. B. Moler. 1977. Computer Methods for Mathematical Computations. Englewood Cliffs, New Jersey: Prentice-Hall Series in Automatic Computation, Prentice-Hall.Google Scholar

  • Gagliardini, P., C. Gourieroux, and E. Renault. 2011. “Efficient Derivative Pricing by Extended Method of Moments.” Econometrica 79 (4): 1181–1232.Web of ScienceGoogle Scholar

  • Gourieroux, C., and J. Jasiak. 2006. “Autoregressive Gamma Process.” Journal of Forecasting 25: 129–152.CrossrefGoogle Scholar

  • Hansen, P. R., and A. Lunde. 2006. “Realized Variance and Market Microstructure Noise (With Discussions).” Journal of Business and Economic Statistics 24: 127–218.CrossrefGoogle Scholar

  • Heston, S. L. 1993. “A Closed-form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options.” The Review of Financial Studies 6 (2): 327–343.CrossrefGoogle Scholar

  • Jacod, J., Y. Li, P. A. Mykland, M. Podolskij, and M. Vetter. 2009. “Microstructure Noise in the Continuous Case: The Pre-averaging Approach.” Stochastic Processes and their Applications 119: 2249–2276.Web of ScienceGoogle Scholar

  • Malliavin, P., and M. E. Mancino. 2002. “Fourier Series Method for Measurement of Multivariate Volatilities.” Finance and Stochastics 6 (1): 49–61.CrossrefGoogle Scholar

  • Mancino, M. E., and S. Ogawa. 2003. “Nonlinear Feedback Effects by Hedging Strategies.” Stochastic Processes and Applications to Mathematical Finance, Proceedings of 2003 Symposium at Ritsumeikan University, World Scientific.Google Scholar

  • Mancino, M. E., and S. Sanfelici. 2008. “Robustness of Fourier Estimator of Integrated Volatility in the Presence of Microstructure Noise.” Computational Statistics and Data Analysis 52 (6): 2966–2989.Web of ScienceGoogle Scholar

  • Mancino, M. E., and S. Sanfelici. 2011. “Covariance Estimation and Dynamic Asset Allocation Under Microstructure Effects via Fourier Methodology.” In Financial Econometrics Modeling, edited by G. N. Gregoriou and R. Pascalau, 3–32. London, UK: Palgrave-Macmillan.Google Scholar

  • Merton, R. 1976. “Option Pricing When the Underlying Stock Returns are Discontinuous.” Journal of Financial Economics 5: 125–144.CrossrefGoogle Scholar

  • Sanfelici, S. 2007. “Calibration of a Nonlinear Feedback Option Pricing Model.” Quantitative Finance 7 (1): 95–110.Web of ScienceCrossrefGoogle Scholar

  • Stentoft, L. 2008. “Option Pricing using Realized Volatility.” Working Paper at CREATES, 1–38. University of Copenhagen.Google Scholar

  • Zhang, L., P. Mykland, and Y. Aït-Sahalia. 2005. “A Tale of Two Time Scales: Determining Integrated Volatility with Noisy High Frequency Data.” Journal of the American Statistical Association 100: 1394–1411.CrossrefGoogle Scholar

About the article

Corresponding author: Simona Sanfelici, University of Parma, Department of Economics, Via J.F. Kennedy 6, 43125 Parma, Italy, e-mail:


Published Online: 2013-07-16

Published in Print: 2014-04-01


This means that (σt2c|σt12)~γ^(δ,βσt12) or, equivalently, that Z~Poiss(βσt12) such that ((σt2c|σt12)|Z)~γ(δ+Z).

For each day in the sample and each time-to-maturity, ATM options are those having moneyness St/K closest to 1. According to this criterion, on each day the set of ATM options contains only one contract for each maturity.

The mispricing index MISP=j=1NO(CjC^jC^j)/j=1NO|CjC^jC^j| ranges from -1 and 1 and indicates, on average, the overpricing (positive MISP) or underpricing (negative MISP) induced by the model. NO represents the total number of options in the sample.


Citation Information: Studies in Nonlinear Dynamics & Econometrics, Volume 18, Issue 2, Pages 103–124, ISSN (Online) 1558-3708, ISSN (Print) 1081-1826, DOI: https://doi.org/10.1515/snde-2012-0075.

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