scholarly journals Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Sangkwon Kim ◽  
Chaeyoung Lee ◽  
Wonjin Lee ◽  
Soobin Kwak ◽  
Darae Jeong ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Experiments ◽  
Operator Splitting ◽  
Three Dimensional ◽  
Nonuniform Grid ◽  
Call Option ◽  
Splitting Scheme ◽  
European Call Option ◽  
Black Scholes

In this study, we present an accurate and efficient nonuniform finite difference method for the three-dimensional (3D) time-fractional Black–Scholes (BS) equation. The operator splitting scheme is used to efficiently solve the 3D time-fractional BS equation. We use a nonuniform grid for pricing 3D options. We compute the three-asset cash-or-nothing European call option and investigate the effects of the fractional-order α in the time-fractional BS model. Numerical experiments demonstrate the efficiency and fastness of the proposed scheme.

scholarly journals Finite Difference Method for the Multi-Asset Black–Scholes Equations

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 391 ◽  
Author(s):  
Sangkwon Kim ◽  
Darae Jeong ◽  
Chaeyoung Lee ◽  
Junseok Kim
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Operator Splitting ◽  
Splitting Method ◽  
Three Dimensional ◽  
Closed Form Solutions ◽  
Operator Splitting Method ◽  
Black Scholes ◽  
The One

In this paper, we briefly review the finite difference method (FDM) for the Black–Scholes (BS) equations for pricing derivative securities and provide the MATLAB codes in the Appendix for the one-, two-, and three-dimensional numerical implementation. The BS equation is discretized non-uniformly in space and implicitly in time. The two- and three-dimensional equations are solved using the operator splitting method. In the numerical tests, we show characteristic examples for option pricing. The computational results are in good agreement with the closed-form solutions to the BS equations.

PENENTUAN HARGA OPSI DENGAN MODEL BLACK-SCHOLES MENGGUNALKAN METODE BEDA HINGGA FORWARD TIME CENTRAL SPACE

2018 ◽  
Vol 1 (1) ◽  
pp. 45
Author(s):  
Werry Febrianti
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Option Price ◽  
Call Option ◽  
Put Option ◽  
Daily Data ◽  
Black Scholes ◽  
One Year ◽  
The Right

Option can be defined as a contract between two sides/parties said party one and party two. Party one has the right to buy or sell of stock to party two. Party two can invest by observe the put option price or call option price on a time period in the option contract. Black-Scholes option solution using finite difference method based on forward time central space (FTCS) can be used as the reference for party two in the investment determining. Option price determining by using Black-Scholes was applied on Samsung stock (SSNLF) by using finite difference method FTCS. Daily data of Samsung stock in one year was processed to obtain the volatility of the stock. Then, the call option and put option are calculated by using FTCS method after discretization on the Black-Scholes model. The value of call option was obtained as $1.457695030014260 and the put option value was obtained as $1.476925604670225.

Pricing options on a mean-reverting asset by the analytical operator splitting method

2021 ◽  
pp. 2150002
Author(s):  
C. F. Lo ◽  
Y. W. He
Keyword(s):  
Operator Splitting ◽  
Splitting Method ◽  
Dynamical Symmetry ◽  
Call Option ◽  
Option Prices ◽  
Pricing Options ◽  
Operator Splitting Method ◽  
European Call Option ◽  
Price Formula ◽  
Black Scholes

In this paper, we propose an operator splitting method to valuate options on the inhomogeneous geometric Brownian motion. By exploiting the approximate dynamical symmetry of the pricing equation, we derive a simple closed-form approximate price formula for a European call option which resembles closely the Black–Scholes price formula for a European vanilla call option. Numerical tests show that the proposed method is able to provide very accurate estimates and tight bounds of the exact option prices. The method is very efficient and robust as well.

A practical finite difference method for the three-dimensional Black–Scholes equation

2016 ◽  
Vol 252 (1) ◽  
pp. 183-190 ◽  
Author(s):  
Junseok Kim ◽  
Taekkeun Kim ◽  
Jaehyun Jo ◽  
Yongho Choi ◽  
Seunggyu Lee ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Three Dimensional ◽  
Black Scholes

scholarly journals A Finite Difference-Spectral Method for Solving the European Call Option Black–Scholes Equation

2021 ◽  
Vol 8 (2) ◽  
pp. 273-278
Author(s):  
Younes Talaei ◽  
Hasan Hosseinzadeh ◽  
Samad Noeiaghdam
Keyword(s):  
Finite Difference ◽  
Numerical Experiment ◽  
Spectral Method ◽  
Difference Method ◽  
Call Option ◽  
Algebraic Equations ◽  
Novel Technique ◽  
European Call Option ◽  
Black Scholes ◽  
Galerkin Spectral Method

In this paper, we present a novel technique based on backward-difference method and Galerkin spectral method for solving Black–Scholes equation. The main propose of this method is to reduce the solution of this problem to the solution of a system of algebraic equations. The convergence order of the proposed method is investigated. Also, we provide numerical experiment to show the validity of proposed method.

Comparison of Split Step Solvers for Multidimensional Schrödinger Problems

2013 ◽  
Vol 13 (2) ◽  
pp. 237-250 ◽  
Author(s):  
Raimondas Čiegis ◽  
Aleksas Mirinavičius ◽  
Mindaugas Radziunas
Keyword(s):  
Finite Difference ◽  
Numerical Experiments ◽  
Operator Splitting ◽  
Three Dimensional ◽  
Finite Difference Schemes ◽  
Alternating Direction Implicit ◽  
One Dimensional ◽  
Alternating Direction ◽  
Discrete Diffraction ◽  
Reaction Potential

Abstract. This paper presents the analysis of the split step solvers for multidimensional Schrödinger problems. The second-order symmetrical splitting techniques are applied. The standard operator splitting is used to split the linear diffraction and reaction/potential processes. The dimension splitting exploits the commuting property of one-dimensional discrete diffraction operators. Alternating Direction Implicit (ADI) and Locally One-Dimensional (LOD) algorithms are constructed and stability is investigated for two- and three-dimensional problems. Compact high-order approximations are applied to discretize diffraction operators. Results of numerical experiments are presented and convergence of finite difference schemes is investigated.

Sign in / Sign up

Export Citation Format

Share Document