Constructing Trinomial Models Based on Cubature Method on Wiener Space: Applications to Pricing Financial Derivatives

TL;DR

This paper extends cubature methods on Wiener space to construct trinomial models for pricing financial derivatives, providing a practical alternative to classical models like Black-Scholes with applications to American options.

Contribution

Introduces a novel application of degree 5 cubature methods on Wiener space to build trinomial models for derivative pricing, enhancing computational efficiency and flexibility.

Findings

Numerical solutions closely match Black-Scholes analytical solutions.

The model effectively prices American-style derivatives.

Method extends to more complex stochastic market models.

Abstract

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.