Solving replication problems in a complete market by orthogonal series expansion

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.