Numerical solution of time-fractional Black–Scholes equation

Koleva, Miglena N.; Vulkov, Lubin G.

doi:10.1007/s40314-016-0330-z

Cited by 43 publications

(22 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A solution for pricing options was obtained by the authors of Song and Wang (2013); Zhang et al (2014) under a TFBSM that employs a θ finite difference scheme with second-order accuracy along with an implicit finite difference arrangement with first-order accuracy. The TFBSM was approximated numerically in Koleva and Vulkov (2017) using a weighted finite difference arrangement.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

2019

View full text Add to dashboard Cite

The price variation of the correlated fractal transmission system is used to deduce the fractional Black-Scholes model that has an α-order time fractional derivative. The fractional Black-Scholes model is employed to price American or European call and put options on a stock paying on a non-dividend basis. Upon encountering fractional differential equations, the efficient and relatively reliable numerical schemes must be obtained for their solution due to fractional derivatives being non-local. The present paper is aimed at determining the numerical solution of the time fractional Black-Scholes model (TFBSM) with boundary conditions for a problem of European option pricing involved with the method of radial basis functions (RBFs), which is a truly meshfree scheme. The TFBSM is discretized in the temporal sense based on finite difference scheme of order O(δt 2−α) for 0 < α < 1 and approximated with the help of the RBF in the spatial derivative terms. In addition, the stability and convergence of the proposed method are theoretically proven. Numerical results illustrate the accuracy and efficiency of the presented technique which is examined in the present study.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

2019

View full text Add to dashboard Cite

show abstract

“…To mix the advantages of both space and time fractionality, spacetime double-fractional diffusion has been introduced and extensively studied from the theoretical point of view [15,23,28,29,31,32,39]; however, it has only been recently considered in financial modeling [8,14,24,25,26]. It features a more complete structure than the simple composition of the time and space fractional models as it exhibits non trivial phenomena including larges jumps and memory effects, which can not be understood as a simple market time re-parametrization of an α-stable process.…”

Section: Introductionmentioning

confidence: 99%

Series representAtion of the Pricing Formula for the EuropeaN Option Driven by Space-Time Fractional Diffusion

Aguilar

Coste

Korbel

2018

FCAA

View full text Add to dashboard Cite

In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. This series formula is obtained from the Mellin-Barnes representation of the option price with help of residue summation in C 2 . We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions. MSC 2010 : 26A33; 34A08; 91B25; 91G20

show abstract

“…Moreover, in this case the fractional derivative turned out to be better for describing the phenomenon. More on the application of the fractional calculus in various fields of science can be found in the papers [ 8 , 9 , 10 , 11 , 12 , 13 , 14 ].…”

Section: Introductionmentioning

confidence: 99%

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Brociek

Chmielowska

Słota

2020

Entropy

View full text Add to dashboard Cite

This paper presents the algorithms for solving the inverse problems on models with the fractional derivative. The presented algorithm is based on the Real Ant Colony Optimization algorithm. In this paper, the examples of the algorithm application for the inverse heat conduction problem on the model with the fractional derivative of the Caputo type is also presented. Based on those examples, the authors are comparing the proposed algorithm with the iteration method presented in the paper: Zhang, Z. An undetermined coefficient problem for a fractional diffusion equation. Inverse Probl. 2016, 32.

show abstract

Numerical solution of time-fractional Black–Scholes equation

Cited by 43 publications

References 12 publications

Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

Numerical analysis of time fractional Black–Scholes European option pricing model arising in financial market

Series representAtion of the Pricing Formula for the EuropeaN Option Driven by Space-Time Fractional Diffusion

Comparison of the Probabilistic Ant Colony Optimization Algorithm and Some Iteration Method in Application for Solving the Inverse Problem on Model With the Caputo Type Fractional Derivative

Contact Info

Product

Resources

About