scholarly journals Laplace Transform Homotopy Perturbation Method for the Two Dimensional Black Scholes Model with European Call Option

2017 ◽  
Vol 22 (1) ◽  
pp. 23 ◽  
Author(s):  
Kamonchat Trachoo ◽  
Wannika Sawangtong ◽  
Panumart Sawangtong
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Two Dimensional ◽  
Call Option ◽  
Homotopy Perturbation ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes

scholarly journals Application of the Generalized Laplace Homotopy Perturbation Method to the Time-Fractional Black–Scholes Equations Based on the Katugampola Fractional Derivative in Caputo Type

Computation ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 33
Author(s):  
Sirunya Thanompolkrang ◽  
Wannika Sawangtong ◽  
Panumart Sawangtong
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Perturbation Method ◽  
Fractional Differential Equations ◽  
Homotopy Perturbation Method ◽  
Call Option ◽  
Homotopy Perturbation ◽  
European Call Option ◽  
Black Scholes ◽  
Fractional Differential

In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations are a powerful tool in studying fractal geometry and fractal dynamics. Fractional differential equations are used in modeling the various important situations or phenomena in the real world such as fluid flow, acoustics, electromagnetic, electrochemistry and material science. There is an important question in finance: “Can the fractional differential equation be applied in the financial market?”. The answer is “Yes”. Due to the self-similar property of the fractional derivative, it can reply to the long-range dependence better than the integer-order derivative. Thus, these advantages are beneficial to manage the fractal structure in the financial market. In this article, the classical Black–Scholes equation with two assets for the European call option is modified by replacing the order of ordinary derivative with the fractional derivative order in the Caputo type Katugampola fractional derivative sense. The analytic solution of time-fractional Black–Scholes European call option pricing equation with two assets is derived by using the generalized Laplace homotopy perturbation method. The used method is the combination of the homotopy perturbation method and generalized Laplace transform. The analytic solution of the time-fractional Black–Scholes equation is carried out in the form of a Mittag–Leffler function. Finally, the effects of the fractional-order in the Caputo type Katugampola fractional derivative to change of a European call option price are shown.

scholarly journals Application of the Laplace Homotopy Perturbation Method to the Black–Scholes Model Based on a European Put Option with Two Assets

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 310 ◽  
Author(s):  
Din Prathumwan ◽  
Kamonchat Trachoo
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Explicit Solution ◽  
Homotopy Perturbation Method ◽  
Approximation Methods ◽  
Numerical Examples ◽  
Homotopy Perturbation ◽  
Put Option ◽  
Black Scholes Model ◽  
Black Scholes

In this paper, the Laplace homotopy perturbation method (LHPM) is applied to obtain the approximate solution of Black–Scholes partial differential equations for a European put option with two assets. Different from all other approximation methods, LHPM provides a simple way to get the explicit solution which is represented in the form of a Mellin–Ross function. The numerical examples represent that the solution from the proposed method is easy and effective.

scholarly journals A New Efficient Method for Solving Two-Dimensional Burgers' Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Hossein Aminikhah
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Efficient Method ◽  
Homotopy Perturbation Method ◽  
Burgers Equation ◽  
Two Dimensional ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
The Laplace Transform

We introduce a new hybrid of the Laplace transform method and new homotopy perturbation method (LTNHPM) that efficiently solves nonlinear two-dimensional Burgers’ equation. Three examples are given to demonstrate the efficiency of the new method.

scholarly journals Nonlinearities distribution Laplace transform-homotopy perturbation method

SpringerPlus ◽  
2014 ◽  
Vol 3 (1) ◽  
pp. 594 ◽  
Author(s):  
Uriel Filobello-Nino ◽  
Hector Vazquez-Leal ◽  
Brahim Benhammouda ◽  
Luis Hernandez-Martinez ◽  
Claudio Hoyos-Reyes ◽  
...  
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation

scholarly journals Markov Chain Monte Carlo Method for Estimating Implied Volatility in Option Pricing

2018 ◽  
Vol 10 (6) ◽  
pp. 108
Author(s):  
Yao Elikem Ayekple ◽  
Charles Kofi Tetteh ◽  
Prince Kwaku Fefemwole
Keyword(s):  
Option Pricing ◽  
Implied Volatility ◽  
Call Option ◽  
Option Prices ◽  
Options Market ◽  
European Call Option ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Real Market ◽  
Independent Path

Using market covered European call option prices, the Independence Metropolis-Hastings Sampler algorithm for estimating Implied volatility in option pricing was proposed. This algorithm has an acceptance criteria which facilitate accurate approximation of this volatility from an independent path in the Black Scholes Model, from a set of finite data observation from the stock market. Assuming the underlying asset indeed follow the geometric brownian motion, inverted version of the Black Scholes model was used to approximate this Implied Volatility which was not directly seen in the real market: for which the BS model assumes the volatility to be a constant. Moreover, it is demonstrated that, the Implied Volatility from the options market tends to overstate or understate the actual expectation of the market. In addition, a 3-month market Covered European call option data, from 30 different stock companies was acquired from Optionistic.Com, which was used to estimate the Implied volatility. This accurately approximate the actual expectation of the market with low standard errors ranging between 0.0035 to 0.0275.

Sign in / Sign up

Export Citation Format

Share Document