Solving Replication Problems in 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 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.
|Date of creation:||Mar 2012|
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- 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 1173-1186, December.