Results 71 to 80 of about 4,903 (187)

A Novel Fourth-Order Finite Difference Scheme for European Option Pricing in the Time-Fractional Black–Scholes Model

Mathematics
This paper addresses the valuation of European options, which involves the complex and unpredictable dynamics of fractal market fluctuations. These are modeled using the α-order time-fractional Black–Scholes equation, where the Caputo fractional ...
Xin Cai, Yihong Wang
doaj   +1 more source

Memory‐Dependent Chaotic Dynamics and Stabilization of a Nonlinear Fractional‐Order Financial System With Optimal Control

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
This study presents an innovative nonlinear fractional‐order financial model that employs Caputo and Caputo–Fabrizio fractional derivatives to represent the dynamic interactions among interest rates, investment demand, price indices, and income/output. The model is formulated as a system of coupled nonlinear differential equations to encapsulate memory‐
Md. Asraful Islam, Razia Sultana, Payer Ahmed, Huaiqin Wu   +3 more
wiley   +1 more source

Numerical Solution of Fractional Black-Scholes Equation by Using the Multivariate Padé Approximation

Acta Physica Polonica A, 2017
In this study, a new application of multivariate Pade approximation method has been used for solving European vanilla call option pricing problem. Pade polynomials have occurred for the fractional Black-Scholes equation, according to the relations of "smaller than", or "greater than", between stock price and exercise price of the option.
Özdemir, Necati, Yavuz, Mehmet
openaire   +3 more sources

Option Pricing in a Fractional Brownian Motion Environment [PDF]

The purpose of this paper is to obtain a fractional Black-Scholes formula for the price of an option for every t in [0,T], a fractional Black-Scholes equation and a risk-neutral valuation theorem if the underlying is driven by a fractional Brownian ...
Cipian Necula
core  

Robust option replication for a Black-Scholes model extended with nondeterministic trends [PDF]

, 2012
Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model.
Kloeden, Peter E., Schoenmakers, John G. M.   +1 more
core  

Correction to Black-Scholes formula due to fractional stochastic volatility

, 2017
Empirical studies show that the volatility may exhibit correlations that decay as a fractional power of the time offset. The paper presents a rigorous analysis for the case when the stationary stochastic volatility model is constructed in terms of a ...
Garnier, Josselin, Solna, Knut
core   +2 more sources

An Efficient Numerical Model for the Black–Scholes Equations

Journal of Applied Mathematics, Volume 2026, Issue 1, 2026.
In this paper, a novel numerical model for the Black–Scholes equations is developed. To address some potential issues that may arise when solving this equation using the conventional model, the original Black–Scholes equation is reformulated as a convection–diffusion equation. The Crank–Nicolson scheme is utilized to discretize the diffusion and source
Yan Zhou, Yunxing Zhang, Yufeng Xu
wiley   +1 more source

An Efficient Numerical Scheme for a Time-Fractional Black–Scholes Partial Differential Equation Derived from the Fractal Market Hypothesis

Fractal and Fractional
Since the early 1970s, the study of Black–Scholes (BS) partial differential equations (PDEs) under the Efficient Market Hypothesis (EMH) has been a subject of active research in financial engineering.
Samuel M. Nuugulu, Frednard Gideon, Kailash C. Patidar   +2 more
doaj   +1 more source

A Framework for Derivative Pricing in the Fractional Black-Scholes Market [PDF]

The aim of this paper is to develop a framework for evaluating derivatives if the underlying of the derivative contract is supposed to be driven by a fractional Brownian motion with Hurst parameter greater than 0.5.
Ciprian Necula
core  

Fundamental Black–Scholes Model, Fractional Binary Approximation, No‐Arbitrage, and Completeness

Journal of Mathematics, Volume 2026, Issue 1, 2026.
Sottinen (2001) constructed a binary model approximating the Black–Scholes (B‐S) model driven by fractional Brownian motion using its Donsker’s type approximation. He further proved that his so‐called fractional binary model has arbitrage opportunities.
Bogny Kenfack Bob James, Mbele Bidima Martin Le Doux, Smritijit Sen   +2 more
wiley   +1 more source