scholarly journals On a free boundary problem for an American put option under the CEV process

2011 ◽  
Vol 24 (7) ◽  
pp. 1191-1198 ◽  
Author(s):  
Miao Xu ◽  
Charles Knessl
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
American Put Option ◽  
Put Option ◽  
Cev Process ◽  
A Free Boundary Problem ◽  
American Put

Valuation of the American put option as a free boundary problem through a high-order difference scheme

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Murat Sari ◽  
Seda Gulen
Keyword(s):  
Free Boundary ◽  
Difference Scheme ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
American Options ◽  
High Order ◽  
Order Difference ◽  
Put Option ◽  
A Free Boundary Problem ◽  
American Put

Abstract Valuation of the American options encountered commonly in finance is quite difficult due to the possibility of early exercise alternatives. Since an exact solution for the American options does not exist, effective numerical methods are needed to understand the behavior of option pricing models. Therefore, in this paper, a new approach based on a high-order difference scheme is proposed to discuss the valuation of an American put option as a free boundary problem. Using a front-fixing approach that transforms the unknown free boundary (optimal stopping) into a fixed one, a sixth-order finite difference scheme (FD6) in space and a third-order strong-stability preserving Runge–Kutta (SSPRK3) in time are applied to the model converted to a nonlinear partial differential equation. The computed results revealed that the combined method is seen to attempt to pull up the capacity of the algorithm to achieve higher accuracy. It is seen that the quantitative and qualitative results produced by the method proposed with minimal computational effort are sufficiently accurate and meaningful. Therefore, this article provides some new insights about the physical characteristics of financial problems and such realistic phenomena.

scholarly journals On the optimal exercise boundary for an American put option

2001 ◽  
Vol 1 (1) ◽  
pp. 39-45 ◽  
Author(s):  
Ghada Alobaidi ◽  
Roland Mallier
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Asymptotic Expansions ◽  
American Put Option ◽  
Optimal Exercise Boundary ◽  
Put Option ◽  
Exercise Boundary ◽  
A Free Boundary Problem ◽  
The Right ◽  
American Put

An American put option is a derivative financial instrument that gives its holder the right but not the obligation to sell an underlying security at a pre-determined price. American options may be exercised at any time prior to expiry at the discretion of the holder, and the decision as to whether or not to exercise leads to a free boundary problem. In this paper, we examine the behavior of the free boundary close to expiry. Working directly with the underlying PDE, by using asymptotic expansions, we are able to deduce this behavior of the boundary in this limit.

Uniqueness of solution to a free boundary problem from combustion with transport

MAT Serie A ◽  
2001 ◽  
Vol 5 ◽  
pp. 37-41
Author(s):  
Claudia Lederman ◽  
Juan Luis Vázquez ◽  
Noemí Wolanski
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Uniqueness Of Solution ◽  
A Free Boundary Problem

EXISTENCE OF PERIODIC SOLUTIONS FOR A FREE BOUNDARY PROBLEM OF HYPERBOLIC TYPE

2008 ◽  
Vol 05 (04) ◽  
pp. 785-806
Author(s):  
KAZUAKI NAKANE ◽  
TOMOKO SHINOHARA
Keyword(s):  
Mathematical Model ◽  
Free Boundary ◽  
Hyperbolic Equation ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Physical Phenomenon ◽  
Hyperbolic Type ◽  
Existence Of Periodic Solutions ◽  
A Free Boundary Problem ◽  
Thin Tape

A free boundary problem that arises from the physical phenomenon of "peeling a thin tape from a domain" is treated. In this phenomenon, the movement of the tape is governed by a hyperbolic equation and is affected by the peeling front. We are interested in the behavior of the peeling front, especially, the phenomenon of self-excitation vibration. In the present paper, a mathematical model of this phenomenon is proposed. The cause of this vibration is discussed in terms of adhesion.

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