Optimal approximations for the free boundary problems of the space-time fractional Black-Scholes equations using a combined physics-informed neural network [PDF]
Scientific ReportsThe combined physics-informed neural network is employed to deal with the free boundary problems of fractional Black-Scholes equations. The solution assumption and the loss function are determined, the transfer learning is borrowed, the combined neural ...
Lina Song +4 more
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An Efficient Numerical Scheme for a Time-Fractional Black–Scholes Partial Differential Equation Derived from the Fractal Market Hypothesis [PDF]
Fractal and FractionalSince 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 +2 more
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The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative [PDF]
Mathematics, 2021 In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation.
Sivaporn Ampun, Panumart Sawangtong
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Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method [PDF]
Abstract and Applied Analysis, 2013 This work deals with the put option pricing problems based on the time-fractional Black-Scholes equation, where the fractional derivative is a so-called modified Riemann-Liouville fractional derivative.
Lina Song, Weiguo Wang
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A New Homotopy Transformation Method for Solving the Fuzzy Fractional Black–Scholes European Option Pricing Equations under the Concept of Granular Differentiability [PDF]
Fractal and Fractional, 2022 The Black–Scholes option pricing model is one of the most significant achievements in modern investment science. However, many factors are constantly fluctuating in the actual financial market option pricing, such as risk-free interest rate, stock price,
Jianke Zhang, Yueyue Wang, Sumei Zhang
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Coupled transform method for time-space fractional Black-Scholes option pricing model
Alexandria Engineering Journal, 2020 This paper presents analytical solutions of a time-space-fractional Black-Scholes model (TSFBSM) using a coupled technique referred to as Fractional Complex Transform (FCT) with the aid of a modified differential transform method.
S.O. Edeki +3 more
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MathematicsThe Black–Scholes model is a fundamental concept in modern financial theory. It is designed to estimate the theoretical value of derivatives, particularly option prices, by considering time and risk factors. In the context of agricultural insurance, this
Astrid Sulistya Azahra +2 more
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Fractional Black-Scholes Model and Technical Analysis of Stock Price [PDF]
Journal of Applied Mathematics, 2013 In the stock market, some popular technical analysis indicators (e.g., Bollinger bands, RSI, ROC, etc.) are widely used to forecast the direction of prices.
Song Xu, Yujiao Yang
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Lie Symmetries and the Invariant Solutions of the Fractional Black–Scholes Equation under Time-Dependent Parameters [PDF]
Fractal and FractionalIn this paper, we consider the time-fractional Black–Scholes model with deterministic, time-varying coefficients. These time parametric constituents produce a model with greater flexibility that may capture empirical results from financial markets and ...
S. Jamal, R. Champala, Suhail Khan
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Galerkin-finite difference method for fractional parabolic partial differential equations [PDF]
MethodsXThe fractional form of the classical diffusion equation embodies the super-diffusive and sub-diffusive characteristics of any flow, depending on the fractional order. This study aims to approximate the solution of parabolic partial differential equations
Md. Shorif Hossan +2 more
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