Numerical solution of fractional Black‐Scholes model of American put option pricing via a nonstandard finite difference method: Stability and convergent analysis

2019 ◽  
Author(s):  
Sedaghat Shahmorad ◽  
Robab Kalantari ◽  
Ahmad Assadzadeh
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Numerical Solution ◽  
Difference Method ◽  
Put Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
American Put ◽  
Nonstandard Finite Difference

scholarly journals A Comparative Study between Implicit and Crank-Nicolson Finite Difference Method for Option Pricing

2020 ◽  
Vol 40 (1) ◽  
pp. 13-27
Author(s):  
Tanmoy Kumar Debnath ◽  
ABM Shahadat Hossain
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
Finite Difference Methods ◽  
Put Option ◽  
Black Scholes ◽  
Implicit Finite Difference ◽  
Difference Methods ◽  
Crank Nicolson

In this paper, we have applied the finite difference methods (FDMs) for the valuation of European put option (EPO). We have mainly focused the application of Implicit finite difference method (IFDM) and Crank-Nicolson finite difference method (CNFDM) for option pricing. Both these techniques are used to discretized Black-Scholes (BS) partial differential equation (PDE). We have also compared the convergence of the IFDM and CNFDM to the analytic BS price of the option. This turns out a conclusion that both these techniques are fairly fruitful and excellent for option pricing. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 13-27

scholarly journals Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Lina Song ◽  
Weiguo Wang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Fractional Derivative ◽  
Option Pricing ◽  
Difference Method ◽  
Put Options ◽  
Put Option ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Liouville Fractional Derivative

This work deals with the put option pricing problems based on the time-fractional Black-Scholes equation, where the fractional derivative is a so-called modified Riemann-Liouville fractional derivative. With the aid of symbolic calculation software, European and American put option pricing models that combine the time-fractional Black-Scholes equation with the conditions satisfied by the standard put options are numerically solved using the implicit scheme of the finite difference method.

Numerical Simulation of Black-Scholes Model by Finite Difference Method

2014 ◽  
Vol 513-517 ◽  
pp. 4090-4093
Author(s):  
Le Le Dong ◽  
Lian Xue ◽  
Lei Wei Lin ◽  
Tuo Chen ◽  
Ming Hui Wu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Empirical Studies ◽  
Financial Derivatives ◽  
Image Simulation ◽  
Pricing Model ◽  
Put Option ◽  
Black Scholes Model ◽  
Black Scholes

Option is the typical representative of financial derivatives, and this paper is focused on the valuation problem of Option. Based on the Black-Scholes Pricing model which had far-reaching influence on the pricing of financial derivatives, researched its theoretical basis and derivation process, and then get the numerical solution via finite difference method and image simulation. And it also includes the part of empirical studies. In research, ZTR and HQ is chosen and analyzed, in order to get the pricing of European put option.

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.

RENORMALIZATION OF BLACK-SCHOLES EQUATION FOR STOCHASTICALLY FLUCTUATING INTEREST RATE

2001 ◽  
Vol 04 (04) ◽  
pp. 621-634
Author(s):  
ALEXANDER G. MUSLIMOV ◽  
NIKOLAI A. SILANT'EV
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Numerical Solution ◽  
Short Term ◽  
Stochastic Component ◽  
Put Option ◽  
Stochastic Fluctuations ◽  
Black Scholes ◽  
The Interest Rate ◽  
American Put

We investigate the effect of stochastic fluctuations of an interest rate on the value of a derivative. We derive the modified Black-Scholes equation that describes evolution of the value of a derivative averaged over an ensemble of stochastic fluctuations of the rate of interest and depends on the "renormalized" values of volatility and rate of interest. We present the explicit expressions for the renormalized volatility and interest rate that incorporate the corrections owing to the short-term stochastic variations of the interest rate. The stochastic component of the interest rate tends to enhance the effective volatility and reduce the effective interest rate that determine an evolution of the option pricing "smoothed out" over the stochastic variations. The results of numerical solution of the modified Black-Scholes equation with the renormalized coefficients are illustrated for an American put option on non-dividend-paying stock.

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.

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