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Solving Replication Problems in Complete Market by Orthogonal Series Expansion


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  • Chaohua Dong


  • Jiti Gao


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We 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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Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 7/12.

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Length: 13 pages
Date of creation: Mar 2012
Date of revision:
Handle: RePEc:msh:ebswps:2012-7

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Keywords: Approximation theory; Black-Scholes theory; complete market; stochastic process; time series;

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  1. 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.
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Cited by:
  1. Shawkat Hammoudeh & Michael McAleer, 2012. "Risk Management and Financial Derivatives: An Overview," Documentos de Trabajo del ICAE 2012-08, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  2. repec:dgr:eureir:1765032527 is not listed on IDEAS
  3. 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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