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首页> 外文期刊>The North American journal of economics and finance >Solving replication problems in a complete market by orthogonal series expansion
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Solving replication problems in a complete market by orthogonal series expansion

机译：通过正交系列扩展解决完整市场中的复制问题

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摘要

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.
机译：我们重新考虑了在一般框架下完整市场中或有债权的复制问题。由于Black-Scholes定价公式存在各种局限性，因此我们提出了一种新方法来获取用于在一般模型中复制索赔的明确的自筹资金交易策略表达式。我们方法的主要优点是，我们建议使用正交展开方法来为与一些常规基础资产流程相关联的自负盈亏策略导出封闭式表达式。结果，获得了欧洲期权的复制策略。与传统的Black-Scholes理论相反，我们从拟议的复制策略中推导了欧式期权的定价公式，该定价公式与Black-Scholes的定价公式完全不同。我们提供了一个执行过程以及数值和经验示例，以展示所提议的交易策略如何在实践中起作用，然后与基于Black-Scholes理论的复制策略进行比较。

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