When 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 Info
To download:
If you experience problems downloading a file, check if you have the
proper application to
view it first. Information about this may be contained
in the File-Format links below. 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.
Publisher Info
Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number
23.
References listed on IDEAS 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.:
Gourieroux, C & Monfort, A & Renault, E, 1993.
"Indirect Inference,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
[Downloadable!] (restricted)
Other versions:
Gourieroux, C. & Monfort, A. & Renault, E., 1992.
"Indirect Inference,"
Papers
92.279, Toulouse - GREMAQ.
Cited by: (explanations, 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.)
Ghysels, E. & Harvey, A. & Renault, E., 1996.
"Stochastic Volatility,"
Cahiers de recherche
9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
Ghysels, E. & Harvey, A. & Renault, E., 1996.
"Stochastic Volatility,"
Cahiers de recherche
9613, Universite de Montreal, Departement de sciences economiques.
[Downloadable!]