Generalized heat diffusion equations with variable coefficients and their fractalization from the Black-Scholes equation

El-Nabulsi, Rami Ahmad; Golmankhaneh, Alireza Khalili

doi:10.1088/1572-9494/abeb05

Cited by 9 publications

(4 citation statements)

References 73 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Previous relations between quantum formulations and game theory were proposed in [43]. Finally, some previous studies suggest that modified diffusion equations might emerge from the BS equation [44]. This point deserves attention in connection with the flow of information in the stock market and its relation with the symmetries of the system.…”

Section: Discussionmentioning

confidence: 90%

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

2021

View full text Add to dashboard Cite

The spontaneous symmetry breaking phenomena applied to Quantum Finance considers that the martingale state in the stock market corresponds to a ground (vacuum) state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena completely ignores the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (martingale). In this paper, we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock markets.

show abstract

Section: Discussionmentioning

confidence: 90%

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

2021

View full text Add to dashboard Cite

show abstract

“…Let a function in two dimensional grid points, that is to say and stands for the index for stock price, and time, respectively. The function can be stated as follows in the subsequent difference scheme [2], [19][20][21][22][23][24]10] etc.…”

Section: Fig 1 An Illustration Of Price Time Meshmentioning

confidence: 99%

A Numerical Approximation on Black-Scholes Equation of Option Pricing

Christain,

Iyai,

Uchenna

2023

ARJOM

View full text Add to dashboard Cite

This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined the Black-Scholes closed form solution and modified Black-Scholes (MBS) partial differential equation using Crank-Nicolson finite difference method. These partial differential equations were approximated to obtain Call and Put option prices. The explicit price of both options is found accordingly. The numerical solutions were compared to the closed form prices of Black-Scholes formula. More so, comparisons of other parameters were discussed for the purpose of investment plans. The computational results shows: increase in stock volatility increases the value of options, when the initial stock price is equal to its strike price the values of call option is higher than the put option. This informs the investor about the behavior of stock prices for the purpose of decision making. Finally, all simulation results presented graphically using MATLAB.

show abstract

“…The obvious way to counter this problem is to introduce an improved model with time parameters to capture the time-sensitivity of price dynamics. In particular, the B-S model with time-dependent parameters plays a crucial role in quantitative finance, since time-dependent volatility influences investment expectations [5]. Several authors, for example, [6,7], have dealt with implementing a time-dependent volatility function.…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetries and the Invariant Solutions of the Fractional Black–Scholes Equation under Time-Dependent Parameters

Jamal,

Champala,

Khan

2024

Fractal Fract

View full text Add to dashboard Cite

In 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 their time-series datasets. We make use of transformations to reduce the underlying model to the classical heat transfer equation. We show that this transformation procedure is possible for a specific risk-free interest rate and volatility of stock function. Furthermore, we reverse these transformations and apply one-dimensional optimal subalgebras of the infinitesimal symmetry generators to establish invariant solutions.

show abstract

Generalized heat diffusion equations with variable coefficients and their fractalization from the Black-Scholes equation

Cited by 9 publications

References 73 publications

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

The Probability Flow in the Stock Market and Spontaneous Symmetry Breaking in Quantum Finance

A Numerical Approximation on Black-Scholes Equation of Option Pricing

Lie Symmetries and the Invariant Solutions of the Fractional Black–Scholes Equation under Time-Dependent Parameters

Contact Info

Product

Resources

About