Exploring Fractional-Order Models in Computational Finance via an Efficient Hybrid Approach
Paper develops efficient hybrid numerical method combining Strang splitting and Lucas-Fibonacci polynomials to solve time-fractional Black-Scholes options.
What it examines
This paper presents a hybrid method for solving the time-fractional Black-Scholes model for traditional and exotic options. It uses a fractional derivative scheme with Strang splitting for time and a meshless method using Lucas and Fibonacci polynomials for space. The study aims to boost accuracy and efficiency in option pricing.
What it concludes
The proposed hybrid method shows improved accuracy and efficiency in pricing both traditional and exotic options. Results indicate that fractional models with meshless techniques better capture market dynamics. This approach can be applied in finance for pricing and risk management, and may extend to other fields using fractional differential equations.
Evidence objects
A new hybrid numerical method fuses fractional Liouville--Caputo derivatives, Strang splitting, and meshless Lucas--Fibonacci discretization, pricing European, American, butterfly spread, double barrier, and digital options with exceptional precision and efficiency.
key_findings bullet 1 · key_findings · validation V0
Researchers report remarkably low error norms using coarser discretizations, significantly reducing computational costs while enhancing robustness, a surprising breakthrough that validates their novel method through comprehensive error analyses and comparisons.
key_findings bullet 2 · key_findings · validation V0
Additional contributions include integrating fractional calculus with innovative penalty methods for free-boundary American options, proposing a time-fractional Black--Scholes model with non-orthogonal polynomials, paving the way for impactful, future market applications.
key_findings bullet 3 · key_findings · validation V0
Employing fractional derivatives and a hybrid numerical framework, this paper presents a $$\text{time-fractional Black-Scholes model}$$ solution that integrates the $$\text{Liouville-Caputo scheme}$$, $\text{Strang splitting}$, and a meshless method based on remarkably robust Lucas--Fibonacci polynomials for vanilla and exotic options. Its originality, novelty, and rigor offer uniquely impactful contribution yielding practical insights.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
- … Mathematical modeling and simulation of financial derivatives have become increasingly popular in recent years. When used correctly, financial … various financial assets, …
Source row: 766 · abstract type: snippet