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.
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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:
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Postal: PO Box 11E, Monash University, Victoria 3800, Australia
Web page: http://www.buseco.monash.edu.au/depts/ebs/
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- 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
- C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
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- 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.
- 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.
- Hammoudeh, S.M. & McAleer, M.J., 2012. "Risk Management and Financial Derivatives: An Overview," Econometric Institute Report EI 2012-14, Erasmus University Rotterdam, Econometric Institute.
- Michael McAleer & Shawkat Hammoudeh, 2012. "Risk Management and Financial Derivatives:An Overview," KIER Working Papers 816, Kyoto University, Institute of Economic Research.
- 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.
- 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.
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