Application of Lie symmetries to solving modified Black-Scholes equation
, 2022 We perform Lie symmetry analysis on the modified Black-Scholes model described as a partial differential equation (PDE). As a result, a new complete Lie symmetry group and infinitesimal generators of the one-dimensional modified fractional Black-Scholes ...
Ramoeletsi, Realeboha +2 more
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RISK-FREE INTERNAL GAINS – BLACK AND SCHOLES RE-EXAMINED [PDF]
In this paper we first show that if a not-necessarily-self-financing portfolio has instantaneously riskless internal gains, then on an infinitesimal time-interval, the increase in the internal gains on the portfolio is the same as the change in the price
Gergei Bana
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Option Pricing: The empirical tests of the Black-Scholes pricing formula and the feed-forward networks [PDF]
In this article we evaluate the pricing performance of the rather simple but revolutionary Black-Scholes model and one of the more complex techniques (neural networks) on the European-style S&P Index call and put options over the period of 1.6.2006 till ...
Michaela Vlasáková Baruníková
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A New Stabled Relaxation Method for Pricing European Options Under the Time-Fractional Vasicek Model. [PDF]
Comput Econ, 2023 Kharrat M, Arfaoui H.
europepmc +1 more source
The Fractional OU Process: Term Structure Theory and Application [PDF]
The paper revisits dynamic term structure models (DTSMs) and proposes a new way in dealing with the limitation of the classical affine models. In particular, this paper expands the flexibility of the DTSMs by applying a fractional Brownian motion as the ...
Esben Hoeg, Per Frederiksen
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The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application [PDF]
The paper revisits dynamic term structure models (DTSMs) and proposes a new way in dealing with the limitation of the classical affine models. In particular, this paper expands the flexibility of the DTSMs by applying a fractional Brownian motion as the ...
Frederiksen, Per H., Høg, Espen P.
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Quantum effects in an expanded Black-Scholes model. [PDF]
Eur Phys J B, 2022 Bhatnagar A, Vvedensky DD.
europepmc +1 more source
Solving the Black-Scholes Partial Differential Equation via the Solution Method for a One-Dimensional Heat Equation: A Pedagogic Approach with a Spreadsheet-Based Illustration [PDF]
, 2019 The derivation of the Black-Scholes option pricing model, if covered in detail, is by far the most complicated among all major models in the finance curriculum.
Clarence C. Y. Kwan
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Numerical Analysis of the Time Fractional Black-Scholes Equation [PDF]
, 2016 时间分数阶Black-Scholes方程在期权定价中有着日益广泛的应用。本文旨在研究该方程的数值解法，构造和分析了两个有效算法。第一个算法结合了时间方向的有限差分和空间方向的谱方法；第二个方法则基于时空Galerkin谱方法。通过引入恰当的Sobolev空间，我们构建了时空变分问题，证明了时空弱问题的适定性。在算法分析方面，我们首先给出两种方法的最优误差估计。然后讨论算法实现技巧，通过选取适当的基函数导出离散问题的线性系统。最后给出一些数值例子验证理论结果。The time fractional ...
刘瑞清
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P A STOCHASTIC BLACK-SCHOLES EQUATION WITH TIME-FRACTIONAL DERIVATIVE ON THE HALF-LINE
, 2016 : We investigate the pricing of options using a modified Black-Scholes equation with a time-fractional derivative and additive white noise on the half-line. We construct the Green function for the initial-boundary value problem adapting the main ideas of
F J Ariza-Hernandez +4 more
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