Abstract
It is important for financial institutions to develop methods to predicttheir exposure and keep their risk under control. Portfolio managers caninsure themselves against the value (of a diversified stock portfolio)dropping below a certain level, by holding in conjunction with the stockportfolio, an index option derivative security. The work reported in thispaper is concerned with the study of non-parametric methods for estimatingthe pricing formula of option derivative securities. Two non-parametricapproaches, the projection pursuit method (PPR) and the local polynomialapproach (LOESS), are studied and compared to a benchmark parametricBlack–Scholes (B–S) approach. The practical relevance of theseapproaches is tested, when applied topricing and hedging of real-world LIFFE FTSE 100 index options from April 1997to November 1997. We compare the two methods by means of constructing ariskless portfolio of stocks, bonds and option derivatives securities. Theportfolio is then delta-hedged on a daily basis using a dynamic tradingstrategy in stocks and bonds during the lifetime of the option instrument.The tests carried out show that both methods generate similar responses,although each method can outperform the others depending on marketconditions, such as, time to maturity of the option instrument.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barria von Bischhoffshausen, J.A. (1997). A general approach to pricing and hedging derivative securities: With an application to LIFFE data. MBA thesis, The Management School, Imperial College of Science Technology and Medicine, University of London.
Barnett W.A., Powell, J. and Tauchen, G. (ed.) (1991). Non Parametric and Semiparametric Methods in Econometrics, and Statistics. Cambridge University Press.
Becker, R. A., Chambers, J.M. and Wilks, A.R. (1988). The New S Language: A Programming Environment for Data Analysis and Graphics. Wadsworth and Brooks, Pacific Grove, California.
Black, F. and Scholes M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.
Blake, D. (1990). Financial Market Analysis. McGraw-Hill, London.
Bossaerts, P. and Hardle, W. (1995). Foreign exchange rates have surprising volatility. First International Conference in High-Frequency Data in Finance, Zurich, March.
Bossaerts, P. and Hillion, P. (1997). Local parametric analysis of hedging in discrete time. Journal of Econometrics, 81, 243–272.
Breiman, L. and Friedman, J.H. (1985). Estimating optimal transformations for multiple regression and correlation. J. Amer. Statist. Assoc., 80, 580–619.
Chiras, D. and Manaster, S. (1978). The information content of stock prices and test of market efficiency. Journal of Financial Economics, 6, 213–234.
Chorafas, D.N. (1996). How to Understand and Use Mathematics for Derivatives. Volumes 1 and 2, Euromoney Publ. plc, London.
Cleveland, W.S. and Devlin, S.J. (1988). Locally-weighted regression: An approach to regression analysis by local fitting. J. Amer. Statist. Assoc., 83, 597–610.
Fan, J. and Gijbels, I. (1996). Local Polynomial Modelling and Its Applications. Chapman-Hall, London.
Friedman, J.H. and Stuetzle, W. (1981). Projection pursuit regression. J. Amer. Statist. Assoc., 76, 817–823.
Gallant, R. (1981). On the bias in flexible functional forms and an essentially unbiased form: The Fourier flexible form. Journal of Econometrics, 15, 211–244.
Hardle, W., Klinke, S. and Turlach, B.A. (1995). XploRe: An Interactive Statistical Computing Environment. Springer-Verlag, New-York.
Hardle, W. (1990). Applied Non-Parametric Regression. Cambridge University Press, New-York.
Hull, J. (1997). Options, Futures, and Other Derivative Securities. Prentice-Hall, International.
Hutchinson, J.M., Lo, A.W. and Poggio, T. (1994). A non-parametric approach to pricing and hedging derivative securities via learning networks. Journal of Finance, XLIX, 851–889.
Kearns, P. (1993). Volatility and the pricing of interest rate derivative claims. Ph.D. thesis, University of Rochester.
Merton, R.C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141–183.
Muller, H-G. (1988). Non-parametric regression analysis of longitudinal data. Lecture Notes in Statistics. Springer-Verlag, Berlin.
Pagan, A. (1996). The econometrics of financial markets. Journal of Empirical Finance, 3, 15–102.
Venables, W.N. and Ripley, B.D. (1994). Modern Applied Statistics with S-Plus., Springer-Verlag, New-York.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Barria, J., Hall, S. A Non-Parametric Approach to Pricing and Hedging Derivative Securities: With an Application to LIFFE Data. Computational Economics 19, 303–322 (2002). https://doi.org/10.1023/A:1015551826141
Issue Date:
DOI: https://doi.org/10.1023/A:1015551826141