Results 1 
8 of
8
Transformation methods for evaluating approximations to the optimal exercise boundary for linear and nonlinear BlackScholes equations
, 2008
"... ..."
A Nonstandard Finite Difference Scheme for the Black–Scholes Equation of Option Pricing
, 2012
"... nonstandard finite difference method, subequation method, Asian options ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
nonstandard finite difference method, subequation method, Asian options
An Accurate Numerical Integrator for the Solution of Black Scholes Financial Model Equation
, 2015
"... In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semidiscretized by the Method of Lines (MOL). The evolving system of ordinary differential equations (ODEs) is integrated numerically b ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semidiscretized by the Method of Lines (MOL). The evolving system of ordinary differential equations (ODEs) is integrated numerically by an Lstable trapezoidallike integrator. Results show accuracy of relative maximum error of order 10^−10.
Supervisor Signature Date Certified by:
, 2013
"... I hereby declare that this submission is my own work towards the award of the M.Phil degree and that, to the best of my knowledge, it contains no material previously published by another person nor material which had been accepted for the award of any other degree of the university, except where du ..."
Abstract
 Add to MetaCart
(Show Context)
I hereby declare that this submission is my own work towards the award of the M.Phil degree and that, to the best of my knowledge, it contains no material previously published by another person nor material which had been accepted for the award of any other degree of the university, except where due acknowledgement had been made in the text.
A highorder compact method for nonlinear BlackScholes option pricing equations of American Options A highorder compact method for nonlinear BlackScholes option pricing equations of American Options
"... Due to transaction costs, illiquid markets, large investors or risks from an unprotected portfolio the assumptions in the classical BlackScholes model become unrealistic and the model results in nonlinear, possibly degenerate, parabolic diffusionconvection equations. Since in general, a closedfo ..."
Abstract
 Add to MetaCart
(Show Context)
Due to transaction costs, illiquid markets, large investors or risks from an unprotected portfolio the assumptions in the classical BlackScholes model become unrealistic and the model results in nonlinear, possibly degenerate, parabolic diffusionconvection equations. Since in general, a closedform solution to the nonlinear BlackScholes equation for American options does not exist (even in the linear case), these problems have to be solved numerically. We present from the literature different compact finite difference schemes to solve nonlinear BlackScholes equations for American options with a nonlinear volatility function. As compact schemes cannot be directly applied to American type options, we use a fixed domain transformation proposed byŠevčovič and show how the accuracy of the method can be increased to order four in space and time.
A Second Order Asymmetric Finite Difference Method for the BlackScholes Equation of European Options
"... Abstract In this paper, we develop a fast numerical scheme for computing the European option pricing problems governed by the BlackScholes equation. We prove that the proposed scheme has second order accuracy in both time and space. Under some restrictions, the stability of the proposed method in ..."
Abstract
 Add to MetaCart
Abstract In this paper, we develop a fast numerical scheme for computing the European option pricing problems governed by the BlackScholes equation. We prove that the proposed scheme has second order accuracy in both time and space. Under some restrictions, the stability of the proposed method in the sense of Von Neumann analysis is presented. It is shown that the proposed scheme has a good performance in the sense of the computational cost compare to the CrankNicolson scheme. Also the accuracy of the proposed scheme is better than the semiimplicit scheme in most cases. Index Terms BlackScholes equation, European option pricing, asymmetric scheme, stability analysis, numerical example