Applications in Finance, Investments, and Banking pp 197-255 | Cite as

# Volatility

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## Abstract

In this chapter we provide an overview of the many volatility predictors that were suggested over time. We first discuss volatility predictors based on historical price and return data. Afterwards, we turn to predictors based on other sources of information. We concentrate on stock return volatility. The methods discussed are, however, equally valid for other assets. Although all predictors are discussed in isolation, it is important that a combination of individual forecasts may sometimes outperform any of its constituents. “The reason that a combined forecast may be preferable is that neither constituent forecast is using all of the data in the available information set in an optimum fashion”.^{1} In the discussion the terms “estimation”, “forecasting” and “prediction” are used interchangeably to emphasize the fact that we see volatility not just as a parameter of some probabilistic model which has to be estimated, but much more as a real-world variable the value of which must be predicted or forecasted.

## Keywords

Stock Return Option Price Conditional Variance Stochastic Volatility Call Option## Preview

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## References

- Akgiray, V. (1989) “Conditional Heteroskedasticity in Time Series of Stock Returns: Evidence and Forecasts,”
*Journal of Business 62*, pp. 55–80.CrossRefGoogle Scholar - Ball, C.A. (1988) Estimation Bias Induced by Discrete Security Prices,
*Journal of Finance 43*, pp. 841–865.CrossRefGoogle Scholar - Ball, C.A. and W.N. Torous (1984) “The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence and Application to Option Pricing,”
*Journal of Business 57*, pp. 97–112.CrossRefGoogle Scholar - Beckers, C.E. (1978) “Variance Prediction: An Empirical Study, University of California Berkeley, Graduate School of Business Administration, Research Program in Finance Working Paper No. 83.Google Scholar
- Beckers, C.E. (1983) Variances of Security Price Returns Based on High, Low, and Closing Prices,”
*Journal of Business*56, pp. 97–112.CrossRefGoogle Scholar - Berndt, E.K., B.H. Hall, R.E. Hall and J.A. Hausman (1974) “Estimation Inference in Nonlinear Structural Models,”
*Annals of Economic and Social Measurement 4*, pp. 653–665.Google Scholar - Black, F. (1976) “The Pricing of Commodity Contracts,”
*Journal of Financial Economics 3*, pp. 167–179.CrossRefGoogle Scholar - Black, F. and M.S. Scholes (1973) “The Pricing of Options and Corporate Liabilities,”
*Journal of Political Economy, 3*, pp. 637–654.CrossRefGoogle Scholar - Bollerslev, T. (1986) “Generalized Autoregressive Conditional Heteroskedasticity,”
*Journal of Econometrics 31*, pp. 307–327.CrossRefGoogle Scholar - Bollerslev, T. (1987) “A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return,”
*Review of Economics and Statistics 59*, pp. 542–547.CrossRefGoogle Scholar - Bollerslev, T., R.Y. Chou and K.F. Kroner (1992) “ARCH Modeling in Finance: A Review of the Theory and Empirical Evidence,”
*Journal of Econometrics 52*, pp. 5–60.CrossRefGoogle Scholar - Bookstaber, R.M. and S. Pomerantz (1989) “An Information-Based Model of Market Volatility,”
*Financial Analysts Journal, November-December*, pp. 37–46.Google Scholar - Brenner, M. and D. Galai (1981) The Properties of the Estimated Risk of Common Stocks Implied by Option Prices, University of California, Berkeley, Graduate School of Business Administration, Research Program in Finance, Working Paper No. 112.Google Scholar
- Burghardt, G. and M. Lane (1990) “How to Tell if Options are Cheap,”
*Journal of Portfolio Management, Winter*, pp. 72–78.Google Scholar - Butler, J.S. and B. Schachter (1986) “Unbiased Estimation of the Black-Scholes Formula,”
*Journal of Financial Economics*15, pp. 341–357.CrossRefGoogle Scholar - Canina, L. and S. Figlewski (1993) “The Information Content of Implied Volatility,”
*Review of Financial Studies, Vol. 6, No. 3*, pp. 659–681.CrossRefGoogle Scholar - Chesney, M. and L.O. Scott (1989) “Pricing European Currency Options: A Comparison of the Modified Black-Scholes Model and a Random Variance Model,”
*Journal of Financial and Quantitative Analysis 24*, pp. 267–284.CrossRefGoogle Scholar - Chiras, D.P. and S. Manaster (1978) “The Informational Content of Option Prices and a Test of Market Efficiency,”
*Journal of Financial Economics 6*, pp. 213–234.CrossRefGoogle Scholar - Cho, D.C. and E.W. Frees (1988) “Estimating the Volatility of Discrete Stock Prices,”
*Journal of Finance 43*, pp. 451–466.CrossRefGoogle Scholar - Choi, J.Y. and K. Shastri (1989) “Bid-Ask Spreads and Volatility Estimates,”
*Journal of Banking and Finance 13*, pp. 207–219.CrossRefGoogle Scholar - Chou, R.Y. (1988) “Volatility Persistence and Stock Valuations: Some Empirical Evidence Using GARCH,”
*Journal of Applied Econometrics 3*, pp. 279–294.CrossRefGoogle Scholar - Christie, A.A. (1982) “The Stochastic Behaviour of Common Stock Variances,”
*Journal of Financial Economics 10*, pp.407–432.CrossRefGoogle Scholar - Cox, J.C. and M. Rubinstein (1985)
*Options Markets*, Prentice-Hall.Google Scholar - Cox, J.C., S.A. Ross and M. Rubinstein (1979) “Option Pricing: A Simplified Approach,”
*Journal of Financial Economics 7*, pp. 229–263.CrossRefGoogle Scholar - Dassios, A. (1992). “Asymtotic Approximations to Stochastic Variance Models,” Discussion Paper London School of Economics.Google Scholar
- Day, T.E. and C.M. Lewis (1988) “The Behaviour of the Volatility Implicit in the Prices of Stock Index Options,”
*Journal of Financial Economics 22*, pp. 103–122.CrossRefGoogle Scholar - Day, T.E. and C.M. Lewis (1990) “Stock Market Volatility and the Information Content of Stock Index Options,”
*Journal of Econometrics 52*, pp. 267–287.CrossRefGoogle Scholar - De Gooijer, J.G. (1989) “Testing Non-Linearities in World Stock Market Prices,”
*Economics Letters 31*, pp. 31–35.CrossRefGoogle Scholar - De Gooijer, J.G. and K. Kumar (1992) “Some Recent Developments in Non-Linear Time Series Modelling, Testing and Forecasting,”
*International Journal of Forecasting 8*, pp. 135–156.CrossRefGoogle Scholar - Dimson, E. and P. Marsh (1990) “Volatility Forecasting without Data-Snooping,”
*Journal of Banking and Finance 14*, pp. 399–421.CrossRefGoogle Scholar - Duan, J.C. (1993) “The GARCH Option Pricing Model,” forthcoming in
*Mathematical Finance*. Google Scholar - Engle, R.F. (1982) “Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation,”
*Econometrica 50*, pp. 987–1007.CrossRefGoogle Scholar - Engle, R.F. and T. Bollerslev (1986) “Modelling the Persistence of Conditional Variances,”
*Econometric Reviews 5*, pp. 1–50.CrossRefGoogle Scholar - Engle, R.F., D.M. Lilien and R.P. Robins (1987) “Estimating Time Varying Risk Premia in the Term Structure: the ARCH-M Model,”
*Econometrica 55*, pp. 391–407.CrossRefGoogle Scholar - Feinstein, S. (1989a) “The Black-Scholes Formula is Nearly Linear in
_{σ}for at-the-money Options; Therefore Implied Volatilities from at-the-money Options are Virtually Unbiased,” Working Paper, Boston University.Google Scholar - Feinstein, S. (1989b) “The Hull and White Implied Volatility: A Theoretical and Empirical Investigation of a Volatility Forecast Implied by the Hull and White Stochastic Volatility Option Pricing Model,” Working Paper Boston University.Google Scholar
- Franses, P.H. (1991) “Some Similarities Between GARCH and Bilinear Time Series Models,” Working Paper Erasmus University Roterdam.Google Scholar
- French, K.R. and R. Roll (1986) “Stock Return Variances: The Arrival of Information and the Reaction of Traders,”
*Journal of Financial Economics 17*, pp. 5–26.CrossRefGoogle Scholar - French, K.R., G.W. Schwert and R.F. Stambaugh (1987) “Expected Stock Returns and Volatility,”
*Journal of Financial Economics 19*, pp. 3–29.CrossRefGoogle Scholar - Garman, M.B. and M.J. Klass (1980) “On the Estimation of Security Price Volatilities from Historical Data,”
*Journal of Business 53*, pp. 67–78.CrossRefGoogle Scholar - Geske, R. and W. Torous (1991) “Volatility Estimation for Option Pricing and Risk Control,” Paper presented at the 2nd International Conference of the Centre for Research in Finance, IMI Group, Rome.Google Scholar
- Granger, C.W.J. (1980)
*Forecasting in Business and Economics*, Academic Press.Google Scholar - Harvey, C.R. and R.E. Whaley (1991) “S&P 100 Index Option Volatility,”
*The Journal of Finance 4*, pp.1551–1561.Google Scholar - Heynen, R.C. (1994 “An Empirical Investigation of Observed Smile Patterns,” forthcoming in
*The Review of Futures Markets*. Google Scholar - Heynen, R.C. and H.M. Kat (1994) “Volatility Prediction: A Comparison of the Stochastic Volatility, GARCH(1,1) and EGARCH(1,1) Model,” Paper presented at the 14th AMEX Options and Derivatives Colloquium, New York.Google Scholar
- Heynen, R.C., A. Kemna and T. Vorst (1994) “Analysis of the Term Structure of Implied Volatilities,”
*Journal of Financial and Quantitative Analysis*. Google Scholar - Hull, J.C. and A. White (1987) “The Pricing of Options on Assets with Stochastic Volatilities,”
*Journal of Finance 42*, pp. 281–300.CrossRefGoogle Scholar - Kat, H.M. (1993a) “Replicating Ordinary Call Options in an Imperfect Market: A Stochastic Simulation Study,” Paper presented at the 13th AMEX Options and Derivatives Colloquium, New York.Google Scholar
- Kat, H.M. (1993b) “Hedging Lookback and Asian Options,” Working Paper MeesPierson Derivatives.Google Scholar
- Kunitomo, N. (1992) “Improving the Parkinson Method of Estimating Security Price Volatilities,”
*Journal of Business 65*, pp. 295–302.Google Scholar - Latane, H. and R. Rendleman (1976) “Standard Deviations of Stock Price Ratios Implied in Option Prices,”
*Journal of Finance 31*, pp. 369–381.Google Scholar - Marsh, T.A. and E.R. Rosenfeld (1986) “Non-Trading, Market Making, and Estimates of Stock Price Volatility,”
*Journal of Financial Economics 15*, pp. 359–372.CrossRefGoogle Scholar - Melino, A. and S.M. Turnbull (1990) “Pricing Foreign Currency Options with Stochastic Volatility,”
*Journal of Econometrics 45*, pp. 239–265.CrossRefGoogle Scholar - Merton, R.C. (1973) “Theory of Rational Option Pricing,”
*Bell Journal of Economics and Management Science 4*, pp. 141–183.CrossRefGoogle Scholar - Merville, L.J. and D.R. Pieptea (1989) “Stock-Price Volatility, Mean-Reverting Diffusion, and Noise,”
*Journal of Financial Economics 24*, pp. 193–214.CrossRefGoogle Scholar - Nelson, D.B. (1990) “ARCH Models as Diffusions Approximations,”
*Journal of Econometrics 45*, 7–38.CrossRefGoogle Scholar - Nelson, D.B. (1991) “Conditional Heteroskedasticity in Asset Returns: A New Approach,”
*Econometrica 59*, pp. 347–370.CrossRefGoogle Scholar - Pagan, A.R. (1984) “Econometric Issues in the Analysis of Regressions with Generated Regressors,”
*International Economic Review 25*, pp. 221–247.CrossRefGoogle Scholar - Pagan, A.R. (1986) “Two Stage and Related Estimators and Their Applications,”
*Review of Economic Studies 53*, pp. 517–538.CrossRefGoogle Scholar - Pagan, A.R. and G.W Schwert (1990) “Alternative Models for Conditional Stock Volatility,”
*Journal of Econometrics 45*, pp. 267–290.CrossRefGoogle Scholar - Parkinson, M. (1980) “The Extreme Value Method for Estimating the Variance of the Rate of Return,”
*Journal of Business 53*, pp. 61–65.CrossRefGoogle Scholar - Patell, J.M. and M.A. Wolfson (1979) “Anticipated Information Releases Reflected in Call Option Prices,”
*Journal of Accounting and Economics 1*, pp. 117–140.CrossRefGoogle Scholar - Poterba, J. and L. Summers (1986) “The Persistence of Volatility and Stock Market Fluctuations,”
*American Economic Review 76*, pp. 1142–1151.Google Scholar - Rahman, A. and L. Kryzanowski (1986) “Alternative Specifications of the Errors in the Black-Scholes Option Pricing Model and Various Implied Variance Formulas,”
*Economics Letters 21*, pp. 61–65.CrossRefGoogle Scholar - Rogers, L.C.G. and S.E. Satchell (1991) “Estimating Variance from High, Low and Closing Prices,”
*Annals of Applied Probability 1*, pp. 504–512.CrossRefGoogle Scholar - Roll, R. (1984) “A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market,”
*Journal of Finance*39, pp. 1127–1139.CrossRefGoogle Scholar - Ruiz, E. (1993) “Quasi-Maximum Likelihood Estimation of Stochastic Volatility Models,” Working Paper, London School of Economics.Google Scholar
- Schmalensee, R. and R.R. Trippi (1978) “Common Stock Volatility Expectations Implied by Option Premia,”
*Journal of Finance 33*, pp. 129–147.CrossRefGoogle Scholar - Schwert, G.W. (1989) “Why Does Stock Market Volatility Change Over Time ?,”
*Journal of Finance 44*, pp. 1115–1153.CrossRefGoogle Scholar - Schwert, G.W. and P.J. Seguin (1990) “Heteroskedasticity in Stock Returns,”
*Journal of Finance 45*, pp. 1129–1155.CrossRefGoogle Scholar - Scott, L.O. (1987) “Option Pricing when the Variance Changes Randomly: Theory, Estimation and an Application,”
*Journal of Financial and Quantitative Analysis 22*, pp. 419–438.CrossRefGoogle Scholar - Scott, L.O. (1991) “Random-Variance Option Pricing: Empirical Tests of the Model and Delta-Sigma Hedging, in: F.J. Fabozzi (ed.),”
*Advances in Futures and Options Research, Vol 5*, JAI Press, pp. 113–135.Google Scholar - Sheikh, A.M. (1991) “Transactions Data Tests of S&P 100 Call Option Pricing,”
*Journal of Financial and Quantitative Analysis 4*, pp. 459–475.CrossRefGoogle Scholar - Stein, J. (1989) “Overreactions in the Options Market,”
*Journal of Finance 44*, pp. 1011–1023.CrossRefGoogle Scholar - Stoll, H.R. and R.E. Whaley (1990) “Stock Market Structure and Volatility,”
*Review of Financial Studies 3*, pp. 37–71.CrossRefGoogle Scholar - Taylor, S.J. and X. Xu (1994) “The Magnitude of Implied Volatility Smiles: Theory and Empirical Evidence for Exchange Rates, forthcoming in”
*The Review of Futures Markets*. Google Scholar - Whaley, R.E. (1982) “Valuation of American Call Options on Dividend-Paying Stocks: Empirical Tests,”
*Journal of Financial Economics 10*, pp. 29–58.CrossRefGoogle Scholar - Wiggins, J.B. (1987) “Option Values under Stochastic Volatility: Theory and Empirical Estimates,”
*Journal of Financial Economics 19*, pp. 351–372.CrossRefGoogle Scholar - Wiggins, J.B. (1991) “Empirical Tests of the Bias and Efficiency of the Extreme Value Variance Estimator for Common Stocks,”
*Journal of Business 64*, pp. 417–432.CrossRefGoogle Scholar