论文标题
基于立方体方法在维纳空间上构建三项模型：定价金融衍生品的应用
Constructing Trinomial Models Based on Cubature Method on Wiener Space: Applications to Pricing Financial Derivatives
论文作者
论文摘要
这项贡献涉及我们在维纳空间上发达的新型立方体方法的扩展。在我们先前的研究中，我们已经表明，立方体公式对于所有多个Stratonovich积分都精确，直至等级等级。实际上，立方方法将求解随机微分方程求解以求解有限的一组普通微分方程。现在，我们将上述方法应用于构建三项式模型并定价不同的金融衍生品。我们将将我们的数值解决方案与黑色和黑色 - choles模型的分析解决方案进行比较。构造的模型在定价美国风格的衍生产品方面具有实际用途，可以扩展到更复杂的随机市场模型。
This contribution deals with an extension to our developed novel cubature methods of degrees 5 on Wiener space. In our previous studies, we have shown that the cubature formula is exact for all multiple Stratonovich integrals up to dimension equal to the degree. In fact, cubature method reduces solving a stochastic differential equation to solving a finite set of ordinary differential equations. Now, we apply the above methods to construct trinomial models and to price different financial derivatives. We will compare our numerical solutions with the Black's and Black--Scholes models' analytical solutions. The constructed model has practical usage in pricing American-style derivatives and can be extended to more sophisticated stochastic market models.
