in this paper two different methods are presented to approximate the solution of the fractional black-scholes equation for valuation of barrier option. also, the two schemes need less computational work in comparison with the traditional methods. in this work, we propose a new generalization of the two-dimensional differential transform method and decomposition method that will extend the appli...

in this paper, a new identification of the lagrange multipliers by means of the sumudu transform, is employed to  btain a quick and accurate solution to the fractional black-scholes equation with the initial condition for a european option pricing problem. undoubtedly this model is the most well known model for pricing financial derivatives. the fractional derivatives is described in caputo sen...

In this paper, Heir-equations method is applied to investigate nonclassical symmetries and new solutions of the Black-Scholes equation. Nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

This paper considers the pricing of a European option using a B, S -market in which the stock price and the asset in the riskless bank account both have hereditary price structures described by the authors of this paper 1999 . Under the smoothness assumption of the payoff function, it is shown that the infinite dimensional Black-Scholes equation possesses a unique classical solution. A spectral...

In this paper, the pricing of a European call option on the underlying asset is performed by using a Monte Carlo method, one of the powerful simulation methods, where the price development of the asset is simulated and value of the claim is computed in terms of an expected value. The proposed approach, applied in Monte Carlo simulation, is based on the Black-Scholes equation which generally def...

in this paper, heir-equations method is applied to investigate nonclassical symmetries and new solutions of the black-scholes equation. nonlinear self-adjointness is proved and infinite number of conservation laws are computed by a new conservation laws theorem.

A Computational Analysis of the Black-Scholes Equations by Yifan Wang This paper explores the most decorated option pricing model in recent history of the financial industry: the Black-Scholes Equation. We will first study the framework of the Black-Scholes Equation in detail by introducing its object of evaluation, distinguished assumptions, and deduction of the Black-Scholes partial different...

Using the dynamic programming principle in optimal stopping theory, we derive a semilinear Black and Scholes type partial differential equation set in a fixed domain for the value of an American (call/put) option. The nonlinearity in the semilinear Black and Scholes equation depends discontinuously on the American option value, so that standard theory for partial differential equation does not ...

Families of explicit solutions are found to a nonlinear Black-Scholes equation which incorporates the feedback-effect of a large trader in case of market illiquidity. The typical solution of these families will have a payoff which approximates a strangle. These solutions were used to test numerical schemes for solving a nonlinear Black-Scholes equation.

This work presents a theoretical analysis for the Black–Scholes equation. Given a terminal condition, the analytical solution of the Black–Scholes equation is obtained by using the Adomian approximate decomposition technique. The mathematical technique employed in this work also has significance in studying some other problems in finance theory.