Sharp error estimate for implicit finite element scheme for American put option

2019 ◽  
Vol 34 (2) ◽  
pp. 85-94 ◽  
Author(s):  
Rafail Z. Dautov ◽  
Alexander V. Lapin
Keyword(s):  
Error Estimate ◽  
Solution Method ◽  
Piecewise Linear ◽  
Finite Element Scheme ◽  
Numerical Solution Method ◽  
Put Option ◽  
Backward Euler ◽  
Degenerate Parabolic ◽  
American Put ◽  
Sharp Error

AbstractWe investigate a numerical solution method for a degenerate parabolic variational inequality that determines American vanilla put pricing. This method is based on piecewise linear finite elements in spatial variables and the backward Euler finite difference in time variable. For the approximate solution, we get sharp error estimate of orderO(h+τ3/4) in the energy norm of the corresponding differential operator.

A DEGENERATE PARABOLIC VARIATIONAL INEQUALITY FOR THE AMERICAN OPTION PRICING PROBLEM

1998 ◽  
Vol 08 (03) ◽  
pp. 485-493
Author(s):  
LORETTA MASTROENI ◽  
MICHELE MATZEU
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Option Pricing ◽  
Weighted Sobolev Spaces ◽  
American Option Pricing ◽  
Ellipticity Condition ◽  
Put Option ◽  
Uniform Ellipticity ◽  
Degenerate Parabolic ◽  
American Put

A formulation in terms of degenerate parabolic variational inequalities for the price of an American put option is stated. The usual uniform ellipticity condition is weakened by the presence of a weight function. Then the appropriate framework is that of some suitable "weighted" Sobolev spaces. One applies a result previously stated by the authors in Ref. 8.

A sharp error estimate for the fast Gauss transform

2006 ◽  
Vol 219 (1) ◽  
pp. 7-12 ◽  
Author(s):  
Xiaoliang Wan ◽  
George Em Karniadakis
Keyword(s):  
Error Estimate ◽  
Gauss Transform ◽  
Fast Gauss Transform ◽  
Sharp Error

The American put option in a one-dimensional diffusion model with level-dependent volatility

Stochastics ◽  
2007 ◽  
Vol 79 (1-2) ◽  
pp. 5-25 ◽  
Author(s):  
P. Babilua ◽  
I. Bokuchava ◽  
B. Dochviri ◽  
M. Shashiashvili
Keyword(s):  
Diffusion Model ◽  
One Dimensional ◽  
American Put Option ◽  
Put Option ◽  
Dimensional Diffusion ◽  
American Put
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