Solving Replication Problems in Complete Market by Orthogonal Series Expansion

Chaohua Dong () and Jiti Gao

No 7/12, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: 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.

Keywords: Approximation theory; Black-Scholes theory; complete market; stochastic process; time series (search for similar items in EconPapers)
JEL-codes: C13 C22 C45 (search for similar items in EconPapers)
Pages: 13 pages
Date: 2012-03
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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Journal Article: Solving replication problems in a complete market by orthogonal series expansion (2013)
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