Solving Replication Problems in Complete Market by Orthogonal Series Expansion
AbstractWe reconsider the replication problem for contingent claims in a complete market under a general framework. Since there are various limitations in the Black-Scholes pricing formula, we propose a new method to obtain an explicit self-financing trading strategy expression for replications of claims in a general model. The departure of our method from the literature is, using an orthogonal expansion of a process related to the proposed trading strategy, we can construct a complete orthonormal basis for the space of cumulative gains in the complete market so that every self-financing strategy can be expressed as a combination of the basis. Hence, a replication strategy is obtained for a European option. Converse to the traditional Black-Scholes theory, we derive a pricing formula for a European option from the proposed replication strategy that is quite different from the Black-Scholes pricing formula. We then provide an implementation procedure to show how the proposed trading strategy works in practice and then compare with a replication strategy based on the Black-Scholes theory.
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.
Bibliographic InfoPaper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 7/12.
Length: 13 pages
Date of creation: Mar 2012
Date of revision:
Contact details of provider:
Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Web page: http://www.buseco.monash.edu.au/depts/ebs/
More information through EDIRC
Other versions of this item:
- Dong, Chaohua & Gao, Jiti, 2013. "Solving replication problems in a complete market by orthogonal series expansion," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 306-317.
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
This paper has been announced in the following NEP Reports:
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.:
- MacBeth, James D & Merville, Larry J, 1979. "An Empirical Examination of the Black-Scholes Call Option Pricing Model," Journal of Finance, American Finance Association, vol. 34(5), pages 1173-86, December.
- repec:dgr:eureir:1765032527 is not listed on IDEAS
- Hammoudeh, Shawkat & McAleer, Michael, 2013.
"Risk management and financial derivatives: An overview,"
The North American Journal of Economics and Finance,
Elsevier, vol. 25(C), pages 109-115.
- Shawkat Hammoudeh & Michael McAleer, 2012. "Risk Management and Financial Derivatives: An Overview," Working Papers in Economics 12/10, University of Canterbury, Department of Economics and Finance.
- Shawkat Hammoudeh & Michael McAleer, 2012. "Risk Management and Financial Derivatives: An Overview," Documentos del Instituto Complutense de AnÃ¡lisis EconÃ³mico 2012-08, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
- Michael McAleer & Shawkat Hammoudeh, 2012. "Risk Management and Financial Derivatives:An Overview," KIER Working Papers 816, Kyoto University, Institute of Economic Research.
- Hammoudeh, S.M. & McAleer, M.J., 2012. "Risk Management and Financial Derivatives: An Overview," Econometric Institute Research Papers EI 2012-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Chaohua Dong & Jiti Gao, 2013. "Orthogonal Expansion of Levy Process Functionals: Theory and Practice," Monash Econometrics and Business Statistics Working Papers 3/13, Monash University, Department of Econometrics and Business Statistics.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Simone Grose).
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.