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Neural network learning of Black-Scholes equation for option pricing
Neural computing & applications (Print)One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes equation is a parabolic partial differential equation which provides an option pricing model.
Daniel de Souza Santos, T. Ferreira
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SSRN Electronic Journal, 2004
In the last three decades increased attention has been paid to the valuation of the contingent claims whose value depend on underlying financial instruments, called securities. One of the most significant achievements in modern investment sciences is the Black-Scholes option pricing model.
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In the last three decades increased attention has been paid to the valuation of the contingent claims whose value depend on underlying financial instruments, called securities. One of the most significant achievements in modern investment sciences is the Black-Scholes option pricing model.
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Mathematical methods in the applied sciences
This paper develops an efficient combined interpolation/finite element approach for solving a three‐dimensional Black‐Scholes problem with stochastic volatility. The technique consists to approximate the time derivative by interpolation whereas the space
E. Ngondiep
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This paper develops an efficient combined interpolation/finite element approach for solving a three‐dimensional Black‐Scholes problem with stochastic volatility. The technique consists to approximate the time derivative by interpolation whereas the space
E. Ngondiep
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A MULTILEVEL APPROACH TO SOLVING THE BLACK–SCHOLES EQUATION [PDF]
International Journal of Theoretical and Applied Finance, 2010 In this manuscript, we develop a multilevel framework for the pricing of a European call option based on multiresolution techniques. In this approach, the Black–Scholes equation is transformed via finite differences into a system of linear equations, where the form of the implicit operator is used to construct coarse grid projectors.
HEDLEY MORRIS, ALFONSO LIMON
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Mathematics and Computers in Simulation, 2020
Prices of options on two assets following two independent geometric Levy processes are governed by a 2D fractional Black–Scholes (BS) equation. The discretization of the BS equation yields linear systems with dense system matrices and the numerical ...
Wen Chen, Song Wang
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Prices of options on two assets following two independent geometric Levy processes are governed by a 2D fractional Black–Scholes (BS) equation. The discretization of the BS equation yields linear systems with dense system matrices and the numerical ...
Wen Chen, Song Wang
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Black-Scholes Differential Equation
2021After deriving the Black-Scholes equation for a call option from the requirement to make a portfolio risk-free, the equation is solved using a number of variable substitutions, which transforms it into a diffusion equation. Using the latter’s Green’s function is then used to value European call options.
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Applicable Analysis, 2020
This paper investigates a time-fractional Black-Scholes equation with an implied volatility which is assumed to be associated with underlying price. Two aspects are considered. One is for the forward problem, i.e.
Xiaoying Jiang, Xiang Xu
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This paper investigates a time-fractional Black-Scholes equation with an implied volatility which is assumed to be associated with underlying price. Two aspects are considered. One is for the forward problem, i.e.
Xiaoying Jiang, Xiang Xu
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An approximation scheme for Black-Scholes equations with delays
Journal of Systems Science and Complexity, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mou-Hsiung Chang +2 more
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Lie symmetry analysis and conservation laws for the time fractional Black–Scholes equation
International Journal of Geometric Methods in Modern Physics (IJGMMP), 2019In this paper, the Lie symmetry algebra admitted by the time fractional Black–Scholes equation is obtained by using the Lie group method. The constructed symmetry generators are investigated to construct a family of exact solutions and conservation laws ...
Youness Chatibi +2 more
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2019
We now are ready to derive the important Black–Scholes Equation [1], which is widely used to determine pricing of Calls and Puts! An outline is given next; details are developed in the next chapter.
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We now are ready to derive the important Black–Scholes Equation [1], which is widely used to determine pricing of Calls and Puts! An outline is given next; details are developed in the next chapter.
openaire +1 more source