Index Option Pricing via Nonparametric Regression

Kung, Ka Po

Author

Kung Ka Po (National University of Singapore, Singapore)

Title

Index Option Pricing via Nonparametric Regression

Source

Econometric Research in Finance, 2022, vol. 7, nr 1, s. 125-142, tab., wykr., bibliogr. 22 POZ.

Keyword

Inwestor finansowy, Model Blacka-Scholesa, Stopa zwrotu akcji, Wycena opcji
Financial investor, Black-Scholes model, Stock rate of returns, Options pricing

Note

JEL classification: C14, C15, G13.
summ.

Abstract

Investors typically use the Black-Scholes (B-S) parametric model to value financial options. However, there is extensive empirical evidence that the B-S model, assuming constant volatility of stock returns, is far from adequate to price options. This paper, using nonparametric regression, incorporates a volatility-adjusting mechanism into the B-S model and prices options on the S&P 500 Index. Specifically, the upgraded B-S model, referred to as the B-S nonparametric model, is equipped with such a mechanism whose function is to assign larger volatilities for larger log returns and smaller volatilities for smaller log returns to characterize volatility clustering, a phenomenon such that large/small log returns tend to be followed by large/small log returns. Using the B-S nonparametric models as a yardstick, our simulation results show that, across the board, the B-S parametric model considerably overprices both call and put options.(original abstract)

Accessibility

The Library of Warsaw School of Economics

Full text

Bibliography

Black, F. Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. "Journal of Political Economy", 81(3):637-654.
Blattberg, R. C. Gonedes, N. J. (1974). A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices." Journal of Business", 47:244-280.
Brooks, C. (2019). Introductory Econometrics for Finance. Cambridge University Press, Cambridge, 4th edition.
Castanias, R. P. (1979). Macroinformation and the Variability of Stock Market Prices. "The Journal of Finance", 34(2):439-450.
Christie, A. A. (1982). The Stochastic Behavior of Common Stock Variances: Value, Leverage and Interest Rate Effects. "Journal of Financial Economics", 10(4):407-432.
Cont, R. (2007). Volatility Clustering in Financial Markets: Empirical Facts and Agent-Based Models. W: Teyssiere, G. Kirman, A. P., editors, Long Memory in Economics, pages 289-309. Springer.
Epanechnikov, V. A. (1969). Non-Parametric Estimation of a Multivariate Probability Density." Theory of Probability & Its Applications", 14(1):153-158.
Fan, J. (2005). A Selective Overview of Nonparametric Methods in Financial Econometrics. "Statistical Science", 20(4):317-337.
Fan, J. Yao, Q. (2003). Nonlinear Time Series: Nonparametric and Parametric Methods. Springer-Verlag, New York.
Ghosh, S. (2018). Kernel Smoothing: Principles, Methods and Applications. John Wiley & Sons.
Hardle, W. (1990). Applied Nonparametric Regression. Cambridge University Press, Cambridge.
Henderson, D. J. Parmeter, C. F. (2015). Applied Nonparametric Econometrics. Cambridge University Press, Cambridge.
Horowitz, J. L. (2009). Semiparametric and Nonparametric Methods in Econometrics. Springer-Verlag, New York.
Hull, J. C. (2018). Options, Futures, and Other Derivatives. Prentice Hall, Upper Saddle River, 9 edition.
Li, Q. Racine, J. S. (2007). Nonparametric Econometrics: Theory and Practice. Princeton University Press.
MacBeth, J. D. Merville, L. J. (1979). An Empirical Examination of the Black-Scholes Call Option Pricing Formula. "The Journal of Finance", 34(5):1173-1186.
Nadaraya, E. A. (1964). On Estimating Regression. "Theory of Probability and Its Applications", 9(1):141-142.
Rosenblatt, M. (1956). Remarks on Some Nonparametric Estimates of a Density Function." Annals of Mathematical Statistics", 27(3):832-837.
Scott, D. W. (2015). Multivariate Density Estimation: Theory, Practice, and Visualization. John Wiley & Sons, New York.
Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman and Hall, London.
Ullah, A. Pagan, A. (1999). Nonparametric Econometrics. Cambridge University Press, Cambridge.
Watson, G. S. (1964). Smooth Regression Analysis. "Sankhya: The Indian Journal of Statistics, Series A "(1961-2002), 26(4):359-372.

Cited by

ISSN

2451-1935
2451-2370

Language

eng

URI / DOI

BazEkon - The Main Library of the Cracow University of Economics

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