Solving replication problems in a complete market by orthogonal series expansion

Chaohua Dong, Jiti Gao

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4 Citations (Scopus)

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 main advantage of our method is that we propose using an orthogonal expansion method to derive a closed-form expression for the self-financing strategy that is associated with some general underlying asset processes. As a consequence, 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 provide an implementation procedure and both numerical and empirical examples to show how the proposed trading strategy works in practice and then compare with a replication strategy based on the Black-Scholes theory.
Original languageEnglish
Pages (from-to)306 - 317
Number of pages12
JournalNorth American Journal of Economics and Finance
Volume25
DOIs
Publication statusPublished - 2013

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