The Compounded BSDE method: A fully-forward method for option pricing and optimal stopping problems in finance
Researchers present the Compound BSDE method, a new deep-learning approach for solving complex financial problems like option pricing and optimal stopping. By reformulating these as systems of backward stochastic differential equations (BSDEs), the method efficiently handles high-dimensional and compound options. The algorithm extends classical techniques, with proven convergence and error estimates. Numerical tests show strong accuracy and speed. While promising, the paper notes limited discussion on real-world data and challenges in extremely high-dimensional cases.
What it examines
This paper introduces the Compound BSDE method, a new deep-learning-based approach for solving option pricing and optimal stopping problems in finance. It reformulates these problems using systems of backward stochastic differential equations, aiming to improve accuracy and efficiency, especially for complex and high-dimensional financial models.
What it concludes
The Compound BSDE method shows strong accuracy and speed for high-dimensional option pricing and optimal stopping problems. It can be used for pricing complex financial products like Bermudan options. Future work may extend its use to other financial models and further improve its error estimates and computational performance.
Evidence objects
Researchers unveil the Compound BSDE method, a groundbreaking deep-learning approach that reformulates complex financial problems, like Bermudan option pricing, as systems of backward stochastic differential equations (BSDEs), enabling efficient solutions in high-dimensional settings.
key_findings bullet 1 · key_findings · validation V0
The new algorithm extends the classical deep BSDE method to handle compound BSDEs, rigorously proving convergence and providing an a posteriori error estimate, ensuring both accuracy and reliability for challenging financial mathematics tasks.
key_findings bullet 2 · key_findings · validation V0
Numerical experiments highlight the methods impressive accuracy and computational efficiency, but the paper notes a need for more real-world data applications and exploration of potential limitations in extremely high-dimensional scenarios.
key_findings bullet 3 · key_findings · validation V0
This paper presents the Compound BSDE method, a fully forward, deep-learning-based approach that reformulates option pricing as a system of BSDEs. Its novel extension to compound BSDEs, a posteriori error estimates, and demonstrated high-dimensional effectiveness mark significant advances, promising impactful applications in quantitative and computational finance.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
We propose the Compound BSDE method, a fully forward, deep-learning-based approach for solving a broad class of problems in financial mathematics, including optimal stopping. The method is based on a reformulation of option pricing problems in terms of a system of backward stochastic differential equations (BSDEs), which offers a new perspective on the numerical treatment of compound options and optimal stopping problems such as Bermudan option pricing. Building on the classical deep BSDE method for a single BSDE, we develop an algorithm for compound BSDEs and establish its convergence properties. In particular, we derive an \emph{a posteriori} error estimate for the proposed method. Numerical experiments demonstrate the accuracy and computational efficiency of the approach, and illustrate its effectiveness for high-dimensional option pricing and optimal stopping problems.
Source row: 1925 · abstract type: unknown