Local parametric analysis of hedging in discrete time
AbstractWhen continuous-time portfolio weights are applied to a discrete-time hedging problem, errors are likely to occur. This paper evaluates the overall importance of the discretization-induced tracking error. It does so by comparing the performance of Black-Scholes hedge ratios against those obtained from a novel estimation procedure, namely local parametric estimation. In the latter, the weights of the duplicating portfolio are estimated by fitting parametric models (in this paper, Black-Scholes) in the neighborhood of the derivative's moneyness and maturity. Local parametric estimation directly incorporates the error from hedging in discrete time. Results are shown where the root mean square tracking error is reduced up to 41% for short-maturity options. The performance can still be improved by combining locally estimated hedge portfolio weights with standard analysis based on historically estimated parameters. The root mean square tracking error is thereby reduced by about 18% for long-maturity options. Plots of the locally estimated volatility parameter against moneyness and maturity reveal the biases of the Black-Scholes model when hedging in discrete time. In particular, there is a sharp ``smile'' effect in the relation between estimated volatility and moneyness for short-maturity options, as well as a significant ``wave'' effect in the relation with maturity for deep out-of-the-money options.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 81 (1997)
Issue (Month): 1 (November)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom
Other versions of this item:
- Bossaerts, P. & Hillion, P., 1995. "Local Parametric Analysis of Hedging in Discrete Time," Discussion Paper 1995-23, Tilburg University, Center for Economic Research.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Gouriéroux, Christian & Monfort, Alain & Tenreiro, Carlos, 1994. "Kernel m-estimators : non parametric diagnostics for structural models," CEPREMAP Working Papers (Couverture Orange) 9405, CEPREMAP.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
- Gibbons, Michael R & Ramaswamy, Krishna, 1993. "A Test of the Cox, Ingersoll, and Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 619-58.
- Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
- HÄRDLE, Wolfgang, 1992.
"Applied nonparametric methods,"
CORE Discussion Papers
1992003, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Hardle, W., 1992. "Applied Nonparametric Methods," Discussion Paper 1992-6, Tilburg University, Center for Economic Research.
- Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation for Research in Economics, Yale University.
- Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9206, Tilburg - Center for Economic Research.
- Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9204, Catholique de Louvain - Institut de statistique.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- Pedro Gozalo & Oliver Linton, 1994. "Local Nonlinear Least Squares Estimation: Using Parametric Information Nonparametrically," Cowles Foundation Discussion Papers 1075, Cowles Foundation for Research in Economics, Yale University.
- Gouriéroux, Christian & Scaillet, O., 1994. "Estimation of the term structure from bond data," CEPREMAP Working Papers (Couverture Orange) 9415, CEPREMAP.
- Cleveland, William S. & Devlin, Susan J. & Grosse, Eric, 1988. "Regression by local fitting : Methods, properties, and computational algorithms," Journal of Econometrics, Elsevier, vol. 37(1), pages 87-114, January.
- Lo, Andrew W. (Andrew Wen-Chuan) & Wang, Jiang, 1959-, 1993.
"Implementing option pricing models when asset returns are predictable,"
3593-93., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Lo, Andrew W & Wang, Jiang, 1995. " Implementing Option Pricing Models When Asset Returns Are Predictable," Journal of Finance, American Finance Association, vol. 50(1), pages 87-129, March.
- Andrew W. Lo & Jiang Wang, 1994. "Implementing Option Pricing Models When Asset Returns Are Predictable," NBER Working Papers 4720, National Bureau of Economic Research, Inc.
- Ait-Sahalia, Yacine, 1996.
"Testing Continuous-Time Models of the Spot Interest Rate,"
Review of Financial Studies,
Society for Financial Studies, vol. 9(2), pages 385-426.
- Yacine Ait-Sahalia, 1995. "Testing Continuous-Time Models of the Spot Interest Rate," NBER Working Papers 5346, National Bureau of Economic Research, Inc.
- Oliver LINTON, .
"Applied nonparametric methods,"
Statistic und Oekonometrie
9312, Humboldt Universitaet Berlin.
- Gourieroux, C & Monfort, A & Renault, E, 1993.
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
- repec:wop:humbsf:1996-68 is not listed on IDEAS
- Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
- P. BOSSAERTS & C. HAFNER & Wolfgang HÄRDLE, 1996. "Foreign Exchange Rates Have Surprising Volatility," SFB 373 Discussion Papers 1996,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- James M. Hutchinson & Andrew W. Lo & Tomaso Poggio, 1994.
"A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks,"
NBER Working Papers
4718, National Bureau of Economic Research, Inc.
- Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. " A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-89, July.
- Peter Bossaerts & Pierre Hillion, 1993. "A Test Of A General Equilibrium Stock Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 311-347.
- Rubinstein, Mark, 1984. " A Simple Formula for the Expected Rate of Return of an Option over a Finite Holding Period," Journal of Finance, American Finance Association, vol. 39(5), pages 1503-09, December.
- repec:wop:humbsf:1995-45 is not listed on IDEAS
- P. BOSSAERTS & Wolfgang HÄRDLE & C. HAFNER, 1995. "A New Method for Volatility Estimation with Applications in Foreign Exchange Rate Series," SFB 373 Discussion Papers 1995,45, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-36, May-June.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.