A new higher order compact finite difference method for generalised Black–Scholes partial differential equation: European call option

2020 ◽  
Vol 363 ◽  
pp. 464-484 ◽  
Author(s):  
Pradip Roul ◽  
V.M.K. Prasad Goura
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Higher Order ◽  
Call Option ◽  
Compact Finite Difference Method ◽  
European Call Option ◽  
Black Scholes

scholarly journals Analisis Lanjut Metode Beda Hingga Eksplisit Untuk Menentukan Harga Opsi

2019 ◽  
Vol 5 (01) ◽  
pp. 41-46
Author(s):  
Wahyudi Sastro
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
A Value ◽  
Black Scholes ◽  
Explicit Finite Difference ◽  
Explicit Finite Difference Method

Abstract. Explicit finite difference method is used to approximate a partial differential equation that is applied to determine the option pricing. The results of this study note that the calculation of option pricing using explicit finite difference method is negative when partition N ≥ 25 with a value of -2.21. Thus, the results of the calculation of option pricing are not convergent and away from the results of analyzing the option pricirng (Black-Scholes) solution. This is because one of the three probabilities Bj = 1- σ2j2Δt  is negative, namely (-0.12) when j ≥ 12 with S ≥ 16.25  (in units). So this explicit finite difference method cannot be used to determine the option pricing. Keywords: Option Pricing, Explicit Finite Difference Method   Abstrak. Metode beda hingga eksplisit digunakan untuk mengaproksimasi suatu persamaan diferensial pasial yang aplikasikan untuk menentukan harga opsi. Hasil penelitian ini diketahui bahwa perhitungan harga opsi dengan menggunakan metode beda hingga eksplisit bernilai negatif pada saat partisi N ≥ 25  dengan nilai -2,21. Dengan demikian, hasil perhitungan harga opsi tidak konvergen dan menjauhi hasil solusi analitik perhitungan harga opsi (Black-Scholes). Hal ini disebabkan karena salah satu ketiga probabilitas Bj = 1- σ2j2Δt yaitu  bernilai negatif yaitu (-0.12) saat j ≥ 12 dengan S ≥ 16.25 (dalam satuan). Sehingga metode beda hingga eksplisit ini tidak dapat digunakan untuk menentukan harga opsi.  Kata Kunci: Harga Opsi, Metode Beda Hingga Eksplisit.

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.

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.

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