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Errors in Implied Volatility Estimation

Published online by Cambridge University Press:  06 April 2009

Ludger Hentschel
Ludger Hentschel
Affiliation:
[email protected], University of Rochester, William E. Simon Graduate School of Business Administration, Rochester, NY 14627.
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Abstract

Estimating implied volatility by inverting the Black-Scholes formula is subject to considerable error when option characteristics are observed with plausible errors. Especially for options away from the money, large changes in volatility produce small changes in option prices. Conversely, small errors in option prices and other option characteristics produce large errors in implied volatilities. In the presence of small measurement errors, unobserved truncation of option prices that violate lower bounds for absence of arbitrage can also lead to systematic volatility smiles. The paper proposes feasible GLS estimators that reduce the noise and bias in implied volatility estimates.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 38 , Issue 4 , December 2003 , pp. 779 - 810
Copyright
Copyright © School of Business Administration, University of Washington 2003

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References

Referrences

Aït-Sahalia, Y., and Lo, A. W. “Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices.” Journal of Finance, 53 (1998), 499–547.CrossRefGoogle Scholar
Amemiya, T.Advanced Econometrics. Cambridge, MA: Harvard Univ. Press (1985).Google Scholar
Andersen, T. G.; Benzoni, L.; and Lund, J. “An Empirical Investigation of Continuous-time Equity Return Models.” Journal of Finance, 57 (2002), 1239–1284.CrossRefGoogle Scholar
Bakshi, G.; Cao, C.; and Chen, Z. “Empirical Performance of Alternative Option Pricing Models.” Journal of Finance, 52 (1997), 2003–2049.CrossRefGoogle Scholar
Bates, D. S. “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options.” Review of Financial Studies, 9 (1996), 69–107.CrossRefGoogle Scholar
Beckers, S. “Standard Deviations Implied in Option Prices as Predictors of Future Stock Price Variability.” Journal of Banking and Finance, 5 (1981), 363–382.CrossRefGoogle Scholar
Black, F., and Scholes, M. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–654.CrossRefGoogle Scholar
Bollerslev, T. “Generalized Autoregressive Conditional Heteroskedasticity.” Journal of Econometrics, 31 (1986), 307–328.CrossRefGoogle Scholar
Boyle, P., and Ananthanarayanan, A. L. “The Impact of Variance Estimation in Option Valuation Models.” Journal of Financial Economics, 5 (1977), 375–387.CrossRefGoogle Scholar
Brandt, M. W., and Wu, T. “Cross-Sectional Tests of Deterministic Volatility Functions.” Unpubl. Paper, Wharton School, Univ. of Pennsylvania, Philadelphia, PA (2001).Google Scholar
Butler, J. S., and Schachter, B. “Unbiased Estimation of the Black-Scholes Formula.” Journal of Financial Economics, 15 (1986), 341–357.CrossRefGoogle Scholar
Canina, L., and Figlewski, S. “The Informational Content of Implied Volatility.” Review of Financial Studies, 6 (1993), 659–681.CrossRefGoogle Scholar
Chiras, D. P., and Manaster, S. “The Information Content of Option Prices and a Test for Market Efficiency.” Journal of Financial Economics, 6 (1978), 213–234.CrossRefGoogle Scholar
Christensen, B. J.; Hansen, C. Strunk; and Prabhala, N. R. “The Telescoping Overlap Problem in Options Data.” Unpubl. Paper, School of Economics and Management, Univ. of Aarhus, Aarhus, Denmark (2001)Google Scholar
Christensen, B. J., and Prabhala, N. R. “The Relation between Implied Volatility and Realized Volatility.” Journal of Financial Economics, 50 (1999), 125–150.CrossRefGoogle Scholar
Christoffersen, P., and Jacobs, K. “The Importance of the Loss Function in Option Pricing.” Unpubl. Paper, McGill Univ., Montreal, Canada (2001).Google Scholar
Das, S. R., and Sundaram, R. K. “Of Smiles and Smirks: A Term Structure Perspective.” Journal of Financial and Quantitative Analysis, 34 (1999), 211–239.CrossRefGoogle Scholar
Day, T. E., and Lewis, C. M. “The Behavior of the Volatility Implicit in the Prices of Stock Index Options.” Journal of Financial Economics, 22 (1988), 103–122.CrossRefGoogle Scholar
Dumas, B.; Fleming, J.; and Whaley, R. E. “Implied Volatility Functions: Empirical Tests.” Journal of Finance, 53 (1998), 2059–2106.CrossRefGoogle Scholar
Ferri, A. “The Structure of Implied Volatility and the Bid-Ask Spread in Option Markets.” Unpubl. Paper, Fox School of Business, Temple Univ., Philadelphia, PA (2001).Google Scholar
Figlewski, S. “Options Arbitrage in Imperfect Markets.” Journal of Finance, 44 (1989), 1289–1311.CrossRefGoogle Scholar
Fleming, J. “The Quality of Market Volatility Forecasts Implied by S&p 100 Index Option Prices.” Journal of Empirical Finance, 5 (1998), 317–345.CrossRefGoogle Scholar
Fleming, J.; Ostdiek, B.; and Whaley, R. E. “Predicting Stock Market Volatility: A New Measure.” Journal of Futures Markets, 15 (1995), 265–302.CrossRefGoogle Scholar
Franks, J. R., and Schwartz, E. S. “The Stochastic Behaviour of Market Variance Implied in the Prices of Index Options.” Economic Journal, 101 (1991), 1460–1475.CrossRefGoogle Scholar
Gallant, A. R.An Introduction to Econometric Theory. Princeton, NJ: Princeton Univ. Press (1997).CrossRefGoogle Scholar
Hajivassiliou, V. A., and Ruud, P. A. “Classical Estimation Methods for LDV Models Using Simulation.” Handbook of Econometrics, Vol. IV. Edited by Engle, Robert F. and McFadden, Daniel L.New York, NY: Elsevier Science B.V. (1994).Google Scholar
Harvey, C. R., and Whaley, R. E.. “S&P 100 Index Option Volatility.” Journal of Finance, 46 (1991), 1551–1561.CrossRefGoogle Scholar
Harvey, C. R., and Whaley, R. E.. “Market Volatility Prediction and the Efficiency of the S&P 100 Index Option Market.” Journal of Financial Economics, 31 (1992), 43–73.CrossRefGoogle Scholar
Heckman, J. “The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models.” Annals of Economic and Social Measurement, 5 (1976), 475–492.Google Scholar
Hentschel, L. “Alternative Models of Asymmetric Volatility in Stock Returns.” Unpubl. Ph.D. Diss., Princeton Univ., Princeton, NJ (1994).Google Scholar
Ho, T., and Stoll, H. R. “Optimal Dealer Pricing under Transactions and Return Uncertainty.” Journal of Financial Economics, 9 (1981), 47–73.CrossRefGoogle Scholar
Jackwerth, J. C., and Rubinstein, M. “Recovery Probability Distribution from Option Prices.” Journal of Finance, 51 (1996), 1611–1631.CrossRefGoogle Scholar
Jones, C. S. “The Dynamics of Stochastic Volatility: Evidence from Underlying and Option Markets.” Unpubl. Paper, Simon School, Univ. of Rochester, Rochester, NY (2001).Google Scholar
Khan, S., and Lewbel, A. “Weighted and Two Stage Least Squares Estimation of Semiparametric Truncated Regression Models.” Unpubl. Paper, Univ. of Rochester, Rochester, NY (2002).Google Scholar
Latané, H. A., and Rendelman, R. J. Jr “Standard Deviations of Stock Price Ratios Implied in Option Prices.” Journal of Finance, 31 (1976), 369–381.CrossRefGoogle Scholar
Ledoit, O.; Santa-Clara, P.; and Yan, S. “Relative Pricing of Options with Stochastic Volatility.” Unpubl. Paper, Anderson School, Univ. of California, Los Angeles, CA (2002).Google Scholar
Luenberger, D. GLinear and Nonlinear Programming, 2nd ed.Reading, MA: Addison-Wesley (1984).Google Scholar
Lyons, R. K. “Tests of the Foreign Exchange Risk Premium Using the Expected Second Moment Implied by Option Pricing.” Journal of International Money and Finance, 7 (1988), 91–108.CrossRefGoogle Scholar
Maddala, G. S.Limited Dependent and Qualitative Variables in Econometrics. New York, NY: Cambridge Univ. Press (1983).CrossRefGoogle Scholar
Manaster, S., and Koehler, G. “The Calculation of Implied Variances form the Black-Scholes Model: A Note.” Journal of Finance, 37 (1982), 227–230.Google Scholar
Merton, R. C. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science, 1 (1973), 141–183.Google Scholar
Olds, E. G. “A Note on the Convolution of Uniform Distributions.” Annals of Mathematical Statistics, 23 (1952), 282–285.CrossRefGoogle Scholar
Pan, J. “The Jump-Risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study.” Journal of Financial Economics, 63 (2002), 3–50.CrossRefGoogle Scholar
Patell, J. M., and Wolfson, M. A.. “Anticipated Information Releases Reflected in Call Option Prices.” Journal of Accounting and Economics, 1 (1979), 117–140.CrossRefGoogle Scholar
Phillips, S. M., and Smith, C. W. Jr “Trading Costs for Listed Options: Implications for Market Efficiency.” Journal of Financial Economics, 8 (1980), 179–189.CrossRefGoogle Scholar
Rubinstein, M. “Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978.” Journal of Finance, 40 (1985), 455–480.CrossRefGoogle Scholar
Schmalensee, R., and Trippi, R. R. “Common Stock Volatility Expectations Implied in Option Premia.” Journal of Finance, 33 (1978), 129–147.CrossRefGoogle Scholar
Scholes, M., and Williams, J. T. “Estimating Betas from Nonsynchronous Data.” Journal of Financial Economics, 5 (1977), 309–327.CrossRefGoogle Scholar
Simonoff, J. S. “Smoothing Methods in Statistics.” New York, NY: Springer-Verlag New York (1996).CrossRefGoogle Scholar
Vijh, A. M. “Liquidity of the CBOE Equity Options.” Journal of Finance, 45 (1990), 1157–1179.CrossRefGoogle Scholar
Whaley, R. E. “Valuation of American Call Options on Dividend-Paying Stocks: Empirical Tests.” Journal of Financial Economics, 10 (1982), 29–58.CrossRefGoogle Scholar
Whaley, R. E. “Derivatives on Market Volatility: Hedging Tools Long Overdue.” Journal of Derivatives, 1 (1993), 71–84.CrossRefGoogle Scholar
White, H. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica, 48 (1980), 817–838.CrossRefGoogle Scholar