A new integral representation of the early exercise boundary for American put options

2000 ◽  
Vol 3 (3) ◽  
pp. 73-96 ◽  
Author(s):  
Thomas Little ◽  
Vijay Pant ◽  
Chunli Hou
Keyword(s):  
Integral Representation ◽  
Put Options ◽  
Early Exercise ◽  
American Put Options ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
American Put

scholarly journals COMPARISON OF NUMERICAL AND ANALYTICAL APPROXIMATIONS OF THE EARLY EXERCISE BOUNDARY OF AMERICAN PUT OPTIONS

2010 ◽  
Vol 51 (4) ◽  
pp. 430-448 ◽  
Author(s):  
M. LAUKO ◽  
D. ŠEVČOVIČ
Keyword(s):  
Numerical Scheme ◽  
Analytical Approximation ◽  
Approximation Formula ◽  
Put Options ◽  
Early Exercise ◽  
Analytical Approximations ◽  
American Put Options ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
American Put

AbstractWe present qualitative and quantitative comparisons of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of American put options paying zero dividends. We analyse the asymptotic behaviour of these methods close to expiration, and introduce a new numerical scheme for computing the early exercise boundary. Our local iterative numerical scheme is based on a solution to a nonlinear integral equation. We compare numerical results obtained by the new method to those of the projected successive over-relaxation method and the analytical approximation formula recently derived by Zhu [‘A new analytical approximation formula for the optimal exercise boundary of American put options’, Int. J. Theor. Appl. Finance9 (2006) 1141–1177].

CALCULATING THE EARLY EXERCISE BOUNDARY OF AMERICAN PUT OPTIONS WITH AN APPROXIMATION FORMULA

2007 ◽  
Vol 10 (07) ◽  
pp. 1203-1227 ◽  
Author(s):  
SONG-PING ZHU ◽  
ZHI-WEI HE
Keyword(s):  
Approximation Formula ◽  
Computational Accuracy ◽  
Put Options ◽  
Early Exercise ◽  
Analytical Approximations ◽  
American Put Options ◽  
Highly Nonlinear ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
Long Lifetime

Accurately as well as efficiently calculating the early exercise boundary is the key to the highly nonlinear problem of pricing American options. Many analytical approximations have been proposed in the past, aiming at improving the computational efficiency and the easiness of using the formula, while maintaining a reasonable numerical accuracy at the same time. In this paper, we shall present an approximation formula based on Bunch and Johnson's work [6]. After clearly pointing out some errors in Bunch and Johnson's paper [6], we will propose an improved approximation formula that can significantly enhance the computational accuracy, particularly for options of long lifetime.

An Early-Exercise-Probability Perspective of American Put Options in the Low-Interest-Rate Era

2014 ◽  
Vol 35 (12) ◽  
pp. 1154-1172 ◽  
Author(s):  
Daniel Wei-Chung Miao ◽  
Yung-Hsin Lee ◽  
Wan-Ling Chao
Keyword(s):  
Interest Rate ◽  
Put Options ◽  
Early Exercise ◽  
American Put Options ◽  
American Put

Integral representation of vega for American put options

2016 ◽  
Vol 19 ◽  
pp. 204-208 ◽  
Author(s):  
Yanchu Liu ◽  
Zhenyu Cui ◽  
Ning Zhang
Keyword(s):  
Integral Representation ◽  
Put Options ◽  
American Put Options ◽  
American Put
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